How to find x or y intercept - PSAT Math
Card 1 of 133
A line has the equation: x+y=1.
What is the y-intercept?
A line has the equation: x+y=1.
What is the y-intercept?
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x+y=1 can be rearranged into: y=-x+1. Using the point-slope form, we can see that the y-intercept is 1.
x+y=1 can be rearranged into: y=-x+1. Using the point-slope form, we can see that the y-intercept is 1.
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A line has the equation: 2x+4y=8.
What is the x-intercept?
A line has the equation: 2x+4y=8.
What is the x-intercept?
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To find the x-intercept, rearrange the equation 2x+4y=8 so that x is isolated:
2x=-4y+8
x=-2y+4
Using the point-slope formula, we see that the x-intercept is 4.
To find the x-intercept, rearrange the equation 2x+4y=8 so that x is isolated:
2x=-4y+8
x=-2y+4
Using the point-slope formula, we see that the x-intercept is 4.
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Which of the following lines does not intersect the line 
?
Which of the following lines does not intersect the line
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Parallel lines never intersect, so you are looking for a line that has the same slope as the one given. The slope of the given line is –4, and the slope of the line in y = –4_x_ + 5 is –4 as well. Since these two lines have equal slopes, they will run parallel and can never intersect.
Parallel lines never intersect, so you are looking for a line that has the same slope as the one given. The slope of the given line is –4, and the slope of the line in y = –4_x_ + 5 is –4 as well. Since these two lines have equal slopes, they will run parallel and can never intersect.
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If the equation of a line is 4_y_ – x = 48, at what point does that line cross the x-axis?
If the equation of a line is 4_y_ – x = 48, at what point does that line cross the x-axis?
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When the equation crosses the x-axis, y = 0. Plug 0 into the equation for y, and solve for x.
4(0) – x = 48, –x = 48, x = –48
When the equation crosses the x-axis, y = 0. Plug 0 into the equation for y, and solve for x.
4(0) – x = 48, –x = 48, x = –48
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Where does the graph of 2x + 3y = 15 cross the x-axis?
Where does the graph of 2x + 3y = 15 cross the x-axis?
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To find the x-intercept, set y=0 and solve for x. This gives an answer of x = 7.5.
To find the x-intercept, set y=0 and solve for x. This gives an answer of x = 7.5.
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The slope of a line is equal to -3/4. If that line intersects the y-axis at (0,15), at what point does it intersect the x-axis?
The slope of a line is equal to -3/4. If that line intersects the y-axis at (0,15), at what point does it intersect the x-axis?
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If the slope of the line m=-3/4, when y=15 and x=0, plug everything into the equation y=mx+b.
Solving for b:
15=(-3/4)*0 + b
b=15
y=-3/4x + 15
To get the x-axis intersect, plug in y=0 and solve for x.
0 = -3/4x + 15
3/4x = 15
3x = 15*4
x = 60/3 = 20
x=20
If the slope of the line m=-3/4, when y=15 and x=0, plug everything into the equation y=mx+b.
Solving for b:
15=(-3/4)*0 + b
b=15
y=-3/4x + 15
To get the x-axis intersect, plug in y=0 and solve for x.
0 = -3/4x + 15
3/4x = 15
3x = 15*4
x = 60/3 = 20
x=20
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Find the y-intercept of 
.
Find the y-intercept of
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To find the y-intercept, set x equal to zero and solve for y.
This gives y = 3(0)2 + 2(0) +7 = 7.
To find the y-intercept, set x equal to zero and solve for y.
This gives y = 3(0)2 + 2(0) +7 = 7.
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If these three points are on a single line, what is the formula for the line?
(3,3)
(4,7)
(5,11)
If these three points are on a single line, what is the formula for the line?
(3,3)
(4,7)
(5,11)
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Formula for a line: y = mx + b
First find slope from two of the points: (3,3) and (4,7)
m = slope = (y2 – y1) / x2 – x1) = (7-3) / (4-3) = 4 / 1 = 4
Solve for b by plugging m and one set of coordinates into the formula for a line:
y = mx + b
11 = 4 * 5 + b
11 = 20 + b
b = -9
y = 4x - 9
Formula for a line: y = mx + b
First find slope from two of the points: (3,3) and (4,7)
m = slope = (y2 – y1) / x2 – x1) = (7-3) / (4-3) = 4 / 1 = 4
Solve for b by plugging m and one set of coordinates into the formula for a line:
y = mx + b
11 = 4 * 5 + b
11 = 20 + b
b = -9
y = 4x - 9
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The slope of a line is 5/8 and the x-intercept is 16. Which of these points is on the line?
The slope of a line is 5/8 and the x-intercept is 16. Which of these points is on the line?
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y = mx + b
x intercept is 16 therefore one coordinate is (16,0)
0 = 5/8 * 16 + b
0 = 10 + b
b = -10
y = 5/8 x – 10
if x = 32
y = 5/8 * 32 – 10 = 20 – 10 = 10
Therefore (32,10)
y = mx + b
x intercept is 16 therefore one coordinate is (16,0)
0 = 5/8 * 16 + b
0 = 10 + b
b = -10
y = 5/8 x – 10
if x = 32
y = 5/8 * 32 – 10 = 20 – 10 = 10
Therefore (32,10)
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Given the line 
, what is the sum of the 
-intercept and the 
-intercept?
Given the line 
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Intercepts occur when a line crosses the 
-axis or the 
-axis. When the line crosses the 
-axis, then 
and 
. When the line crosses the 
-axis, then 
and 
. The intercept points are 
and 
. So the 
-intercept is 
and the 
intercept is 
and the sum is 
.
Intercepts occur when a line crosses the 
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What is the y intercept of the following function of x?
y = 3x
What is the y intercept of the following function of x?
y = 3x
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The answer is 0 because in slope intercept form, y = mx + b; b is the y intercept. In this case b = 0.
The answer is 0 because in slope intercept form, y = mx + b; b is the y intercept. In this case b = 0.
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What is the x-intercept of a line with a slope of 5 and y-intercept of 3.5?
What is the x-intercept of a line with a slope of 5 and y-intercept of 3.5?
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To solve this, first find the equation of our line. The form of the question gives it to us very directly. We can use the slope-intercept form (y = mx + b).
y = 5x + 3.5
The x-intercept is found by setting y = 0, because that will give us the x-value at which the line crosses the x-axis.
0 = 5x + 3.5; –3.5 = 5x; x = –3.5 / 5 or –0.7. The point will be (–0.7, 0)
To solve this, first find the equation of our line. The form of the question gives it to us very directly. We can use the slope-intercept form (y = mx + b).
y = 5x + 3.5
The x-intercept is found by setting y = 0, because that will give us the x-value at which the line crosses the x-axis.
0 = 5x + 3.5; –3.5 = 5x; x = –3.5 / 5 or –0.7. The point will be (–0.7, 0)
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Determine the y-intercept of the following line:
3x+6y=9
Determine the y-intercept of the following line:
3x+6y=9
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The y-intercept occurs when x=0
3x+6y=9
3(0)+6y=9
0+6y=9
y = $\frac{9}{6}$=1.5
The y-intercept occurs when x=0
3x+6y=9
3(0)+6y=9
0+6y=9
y = $\frac{9}{6}$=1.5
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At what point does the graph 3y-2x=31 cross the 
-axis?
At what point does the graph 3y-2x=31 cross the
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The graph crosses the 
-axis where x=0. So plugging in and solving yields $\frac{31}{3}$.
The graph crosses the
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What are the 
-intercept(s) of the following line:
What are the
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We can factor 
and set 
equal to zero to determine the 
-intercepts.
satisfies this equation.
Therefore our 
-intercepts are 
and 
.
We can factor
Therefore our
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Find the x-intercepts of $25x^{2}$$+4y^{2}$ = 9.
Find the x-intercepts of $25x^{2}$$+4y^{2}$ = 9.
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To find the x-intercepts, plug y=0 into the equation and solve for x.
$25x^{2}$ + 4cdot $0^{2}$ = 9
$25x^{2}$ = 9
$x^{2}$ = $\frac{9}{25}$
x = pm $\frac{3}{5}$
Don't forget that there are two solutions, both negative and positive!
To find the x-intercepts, plug y=0 into the equation and solve for x.
$25x^{2}$ + 4cdot $0^{2}$ = 9
$25x^{2}$ = 9
$x^{2}$ = $\frac{9}{25}$
x = pm $\frac{3}{5}$
Don't forget that there are two solutions, both negative and positive!
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Where does the line given by y=3(x-4)-9 intercept the 
-axis?
Where does the line given by y=3(x-4)-9 intercept the 
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First, put in slope-intercept form.
y=3x-21.
To find the 
-intercept, set 
and solve for 
.
First, put in slope-intercept form.
y=3x-21.
To find the
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A line with the exquation $y=x^2$+3x+c passes through the point 
. What is the 
-intercept?
A line with the exquation $y=x^2$+3x+c passes through the point
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By plugging in the coordinate, we can figure out that 
. The 
-Intercept is when 
, plugging in 0 for 
gives us 
.
By plugging in the coordinate, we can figure out that
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The slope of a line is m=\frac{4}{3}$. The line passes through (2,7). What is the x-intercept?
The slope of a line is m=\frac{4}{3}$. The line passes through (2,7). What is the x-intercept?
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The equation for a line is:
y=mx+b, or in this case
y=\frac{4}{3}$x+b
We can solve for b by plugging in the values given
7=\frac{4}{3}$times 2+b
7=2$\frac{2}{3}$+b
b=7-2$\frac{2}{3}$=4$\frac{1}{3}$
Our line is now
y=\frac{4}{3}$x+4$\frac{1}{3}$
Our x-intercept occurs when y=0, so plugging in and solving for x:
0=\frac{4}{3}$x+4$\frac{1}{3}$
-$\frac{13}{3}$=\frac{4}{3}$x
x=-$\frac{13}{4}$
The equation for a line is:
y=mx+b, or in this case
y=\frac{4}{3}$x+b
We can solve for b by plugging in the values given
7=\frac{4}{3}$times 2+b
7=2$\frac{2}{3}$+b
b=7-2$\frac{2}{3}$=4$\frac{1}{3}$
Our line is now
y=\frac{4}{3}$x+4$\frac{1}{3}$
Our x-intercept occurs when y=0, so plugging in and solving for x:
0=\frac{4}{3}$x+4$\frac{1}{3}$
-$\frac{13}{3}$=\frac{4}{3}$x
x=-$\frac{13}{4}$
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Which of the following lines does not intersect the line ?
Which of the following lines does not intersect the line
Tap to reveal answer
Parallel lines never intersect, so you are looking for a line that has the same slope as the one given. The slope of the given line is –4, and the slope of the line in y = –4_x_ + 5 is –4 as well. Since these two lines have equal slopes, they will run parallel and can never intersect.
Parallel lines never intersect, so you are looking for a line that has the same slope as the one given. The slope of the given line is –4, and the slope of the line in y = –4_x_ + 5 is –4 as well. Since these two lines have equal slopes, they will run parallel and can never intersect.
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