How to find out if a point is on a line with an equation - PSAT Math
Card 1 of 42
In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?
In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?
Tap to reveal answer
The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:
2_x_ - 3(1) = 5
2_x_ - 3 = 5
2_x_ = 8
x = 4. So the missing x-value on line l is 4.
The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:
2_x_ - 3(1) = 5
2_x_ - 3 = 5
2_x_ = 8
x = 4. So the missing x-value on line l is 4.
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The equation of a line is: 2x + 9y = 71
Which of these points is on that line?
The equation of a line is: 2x + 9y = 71
Which of these points is on that line?
Tap to reveal answer
Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.
2(x) + 9(7) = 71
2x + 63 = 71
2x = 8
x = 4
Therefore the answer is (4, 7)
Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.
2(x) + 9(7) = 71
2x + 63 = 71
2x = 8
x = 4
Therefore the answer is (4, 7)
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5x+25y = 125
Which point lies on this line?
5x+25y = 125
Which point lies on this line?
Tap to reveal answer
5x+25y = 125
Test the coordinates to find the ordered pair that makes the equation of the line true:
(5,4)
5 (5) + 25 (4) = 25 + 100 = 125
(1,5)
5(1)+25(5)= 5+125=130
(5,1)
5(5)+25(1)= 25+25=50
(5,5)
5(5)+25(5)= 25+125=150
(1,4)
5(1)+25(4)= 5+100=105
5x+25y = 125
Test the coordinates to find the ordered pair that makes the equation of the line true:
(5,4)
5 (5) + 25 (4) = 25 + 100 = 125
(1,5)
5(1)+25(5)= 5+125=130
(5,1)
5(5)+25(1)= 25+25=50
(5,5)
5(5)+25(5)= 25+125=150
(1,4)
5(1)+25(4)= 5+100=105
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Which of the following lines contains the point (8, 9)?
Which of the following lines contains the point (8, 9)?
Tap to reveal answer
In order to find out which of these lines is correct, we simply plug in the values x=8 and y=9 into each equation and see if it balances.
The only one for which this will work is 3x-6=2y
In order to find out which of these lines is correct, we simply plug in the values x=8 and y=9 into each equation and see if it balances.
The only one for which this will work is 3x-6=2y
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Points D and E lie on the same line and have the coordinates 
and 
, respectively. Which of the following points lies on the same line as points D and E?
Points D and E lie on the same line and have the coordinates
Tap to reveal answer
The first step is to find the equation of the line that the original points, D and E, are on. You have two points, so you can figure out the slope of the line by plugging the points into the equation
.
Therefore, you can get an equation in the line in point-slope form, which is
.
Plug in the answer options, and you will find that only the point 
solves the equation.
The first step is to find the equation of the line that the original points, D and E, are on. You have two points, so you can figure out the slope of the line by plugging the points into the equation
Therefore, you can get an equation in the line in point-slope form, which is
Plug in the answer options, and you will find that only the point
← Didn't Know|Knew It →
Which of the following points is on the line given by the equation 
?
Which of the following points is on the line given by the equation
Tap to reveal answer
In order to solve this, try each of the answer choices in the equation:
For example, when we try (3,4), we find:
This does not work. When we try all the choices, we find that only (2,4) works:
In order to solve this, try each of the answer choices in the equation:
For example, when we try (3,4), we find:
This does not work. When we try all the choices, we find that only (2,4) works:
← Didn't Know|Knew It →
In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?
In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?
Tap to reveal answer
The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:
2_x_ - 3(1) = 5
2_x_ - 3 = 5
2_x_ = 8
x = 4. So the missing x-value on line l is 4.
The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:
2_x_ - 3(1) = 5
2_x_ - 3 = 5
2_x_ = 8
x = 4. So the missing x-value on line l is 4.
← Didn't Know|Knew It →
The equation of a line is: 2x + 9y = 71
Which of these points is on that line?
The equation of a line is: 2x + 9y = 71
Which of these points is on that line?
Tap to reveal answer
Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.
2(x) + 9(7) = 71
2x + 63 = 71
2x = 8
x = 4
Therefore the answer is (4, 7)
Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.
2(x) + 9(7) = 71
2x + 63 = 71
2x = 8
x = 4
Therefore the answer is (4, 7)
← Didn't Know|Knew It →
5x+25y = 125
Which point lies on this line?
5x+25y = 125
Which point lies on this line?
Tap to reveal answer
5x+25y = 125
Test the coordinates to find the ordered pair that makes the equation of the line true:
(5,4)
5 (5) + 25 (4) = 25 + 100 = 125
(1,5)
5(1)+25(5)= 5+125=130
(5,1)
5(5)+25(1)= 25+25=50
(5,5)
5(5)+25(5)= 25+125=150
(1,4)
5(1)+25(4)= 5+100=105
5x+25y = 125
Test the coordinates to find the ordered pair that makes the equation of the line true:
(5,4)
5 (5) + 25 (4) = 25 + 100 = 125
(1,5)
5(1)+25(5)= 5+125=130
(5,1)
5(5)+25(1)= 25+25=50
(5,5)
5(5)+25(5)= 25+125=150
(1,4)
5(1)+25(4)= 5+100=105
← Didn't Know|Knew It →
Which of the following lines contains the point (8, 9)?
Which of the following lines contains the point (8, 9)?
Tap to reveal answer
In order to find out which of these lines is correct, we simply plug in the values x=8 and y=9 into each equation and see if it balances.
The only one for which this will work is 3x-6=2y
In order to find out which of these lines is correct, we simply plug in the values x=8 and y=9 into each equation and see if it balances.
The only one for which this will work is 3x-6=2y
← Didn't Know|Knew It →
Points D and E lie on the same line and have the coordinates and , respectively. Which of the following points lies on the same line as points D and E?
Points D and E lie on the same line and have the coordinates
Tap to reveal answer
The first step is to find the equation of the line that the original points, D and E, are on. You have two points, so you can figure out the slope of the line by plugging the points into the equation
.
Therefore, you can get an equation in the line in point-slope form, which is
.
Plug in the answer options, and you will find that only the point solves the equation.
The first step is to find the equation of the line that the original points, D and E, are on. You have two points, so you can figure out the slope of the line by plugging the points into the equation
Therefore, you can get an equation in the line in point-slope form, which is
Plug in the answer options, and you will find that only the point
← Didn't Know|Knew It →
Which of the following points is on the line given by the equation ?
Which of the following points is on the line given by the equation
Tap to reveal answer
In order to solve this, try each of the answer choices in the equation:
For example, when we try (3,4), we find:
This does not work. When we try all the choices, we find that only (2,4) works:
In order to solve this, try each of the answer choices in the equation:
For example, when we try (3,4), we find:
This does not work. When we try all the choices, we find that only (2,4) works:
← Didn't Know|Knew It →
In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?
In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?
Tap to reveal answer
The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:
2_x_ - 3(1) = 5
2_x_ - 3 = 5
2_x_ = 8
x = 4. So the missing x-value on line l is 4.
The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:
2_x_ - 3(1) = 5
2_x_ - 3 = 5
2_x_ = 8
x = 4. So the missing x-value on line l is 4.
← Didn't Know|Knew It →
The equation of a line is: 2x + 9y = 71
Which of these points is on that line?
The equation of a line is: 2x + 9y = 71
Which of these points is on that line?
Tap to reveal answer
Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.
2(x) + 9(7) = 71
2x + 63 = 71
2x = 8
x = 4
Therefore the answer is (4, 7)
Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.
2(x) + 9(7) = 71
2x + 63 = 71
2x = 8
x = 4
Therefore the answer is (4, 7)
← Didn't Know|Knew It →
5x+25y = 125
Which point lies on this line?
5x+25y = 125
Which point lies on this line?
Tap to reveal answer
5x+25y = 125
Test the coordinates to find the ordered pair that makes the equation of the line true:
(5,4)
5 (5) + 25 (4) = 25 + 100 = 125
(1,5)
5(1)+25(5)= 5+125=130
(5,1)
5(5)+25(1)= 25+25=50
(5,5)
5(5)+25(5)= 25+125=150
(1,4)
5(1)+25(4)= 5+100=105
5x+25y = 125
Test the coordinates to find the ordered pair that makes the equation of the line true:
(5,4)
5 (5) + 25 (4) = 25 + 100 = 125
(1,5)
5(1)+25(5)= 5+125=130
(5,1)
5(5)+25(1)= 25+25=50
(5,5)
5(5)+25(5)= 25+125=150
(1,4)
5(1)+25(4)= 5+100=105
← Didn't Know|Knew It →
Which of the following lines contains the point (8, 9)?
Which of the following lines contains the point (8, 9)?
Tap to reveal answer
In order to find out which of these lines is correct, we simply plug in the values x=8 and y=9 into each equation and see if it balances.
The only one for which this will work is 3x-6=2y
In order to find out which of these lines is correct, we simply plug in the values x=8 and y=9 into each equation and see if it balances.
The only one for which this will work is 3x-6=2y
← Didn't Know|Knew It →
Points D and E lie on the same line and have the coordinates and , respectively. Which of the following points lies on the same line as points D and E?
Points D and E lie on the same line and have the coordinates
Tap to reveal answer
The first step is to find the equation of the line that the original points, D and E, are on. You have two points, so you can figure out the slope of the line by plugging the points into the equation
.
Therefore, you can get an equation in the line in point-slope form, which is
.
Plug in the answer options, and you will find that only the point solves the equation.
The first step is to find the equation of the line that the original points, D and E, are on. You have two points, so you can figure out the slope of the line by plugging the points into the equation
Therefore, you can get an equation in the line in point-slope form, which is
Plug in the answer options, and you will find that only the point
← Didn't Know|Knew It →
Which of the following points is on the line given by the equation ?
Which of the following points is on the line given by the equation
Tap to reveal answer
In order to solve this, try each of the answer choices in the equation:
For example, when we try (3,4), we find:
This does not work. When we try all the choices, we find that only (2,4) works:
In order to solve this, try each of the answer choices in the equation:
For example, when we try (3,4), we find:
This does not work. When we try all the choices, we find that only (2,4) works:
← Didn't Know|Knew It →
In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?
In the xy -plane, line l is given by the equation 2_x_ - 3_y_ = 5. If line l passes through the point (a ,1), what is the value of a ?
Tap to reveal answer
The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:
2_x_ - 3(1) = 5
2_x_ - 3 = 5
2_x_ = 8
x = 4. So the missing x-value on line l is 4.
The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:
2_x_ - 3(1) = 5
2_x_ - 3 = 5
2_x_ = 8
x = 4. So the missing x-value on line l is 4.
← Didn't Know|Knew It →
The equation of a line is: 2x + 9y = 71
Which of these points is on that line?
The equation of a line is: 2x + 9y = 71
Which of these points is on that line?
Tap to reveal answer
Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.
2(x) + 9(7) = 71
2x + 63 = 71
2x = 8
x = 4
Therefore the answer is (4, 7)
Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.
2(x) + 9(7) = 71
2x + 63 = 71
2x = 8
x = 4
Therefore the answer is (4, 7)
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