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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1576 : Intermediate Geometry

What is the y-intercept of the line with the equation $y-8=\frac{2}{3}(x-9)$ ?

Possible Answers:

(0, 2)

(0, -10)

(0, 8)

(0, -6)

Correct answer:

(0, 2)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

$y-8=\frac{2}{3}(x-9)$

$y-8=\frac{2}{3}x-6$

$y=\frac{2}{3}x+2$

Since, b=2 , the y-intercept must be located at (0,2)

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Example Question #1577 : Intermediate Geometry

What is the y-intercept of a line that has the equation $y-10=\frac{3}{4}(x+12)$ ?

Possible Answers:

(0, -9)

(0, 15)

(0, -4)

(0, 19)

Correct answer:

(0, 19)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

$y-10=\frac{3}{4}(x+12)$

$y-10=\frac{3}{4}x+9$

$y=\frac{3}{4}x+19$

Since, b=19 , the y-intercept must be located at (0,19)

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Example Question #1578 : Intermediate Geometry

What is the y-intercept of a line that has the equation $y+12=-\frac{1}{5}(x-20)$ ?

Possible Answers:

(0, -18)

$(0, -\frac{1}{5})$

(0, 14)

(0, -8)

Correct answer:

(0, -8)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

$y+12=-\frac{1}{5}(x-20)$

$y+12=-\frac{1}{5}x+4$

$y=-\frac{1}{5}x-8$

Since, b=-8 , the y-intercept must be located at (0,-8) .

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Example Question #1571 : Intermediate Geometry

What is the y-intercept of the line that has the equation $y-8=\frac{1}{10}(x+200)$ ?

Possible Answers:

(0, 28)

(0, 20)

(0, 18)

(0, 32)

Correct answer:

(0, 28)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

$y-8=\frac{1}{10}(x+200)$

$y-8=\frac{1}{10}x+20$

$y=\frac{1}{10}x+28$

Since, b=28 , the y-intercept must be located at (0,28) .

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Example Question #1571 : Intermediate Geometry

What is the y-intercept of the line that has the equation y-7=-2(x-10) ?

Possible Answers:

(0, -17)

(0, 27)

(0, 18)

(0, 24)

Correct answer:

(0, 27)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

y-7=-2(x-10)

y-7=-2x+20

y=-2x+27

Since, b=27 , the y-intercept must be located at (0,27) .

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Example Question #1581 : Intermediate Geometry

Find the y-intercept of the line that has the equation y+15=-7(x-2) .

Possible Answers:

(0, -13)

(0, -3)

(0, -19)

(0, -1)

Correct answer:

(0, -1)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

y+15=-7(x-2)

y+15=-7x+14

y=-7x-1

Since, b=-1 , the y-intercept must be located at (0,-1) .

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Example Question #1582 : Intermediate Geometry

What is the y-intercept of a line that has the equation y-24=-8(x+1) ?

Possible Answers:

(0, 24)

(0, 8)

(0, 10)

(0, 16)

Correct answer:

(0, 16)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

y-24=-8(x+1)

y-24=-8x-8

y=-8x+16

Since, b=16 , the y-intercept must be located at (0,16) .

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Example Question #1583 : Intermediate Geometry

What is the y-intercept of a line that has the equation $y+29=-\frac{1}{4}(x+36)$ ?

Possible Answers:

(0,-38)

(0, 2)

(0, -29)

(0, -18)

Correct answer:

(0,-38)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

$y+29=-\frac{1}{4}(x+36)$

$y+29=-\frac{1}{4}x-9$

$y=-\frac{1}{4}x-38$

Since, b=-38 , the y-intercept must be located at (0,-38) .

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Example Question #1584 : Intermediate Geometry

What is the y-intercept of the line with the equation?

$y-10=-20(x+\frac{1}{4})$

Possible Answers:

(0, 24)

(0, 18)

(0, 21)

(0, 5)

Correct answer:

(0, 5)

Explanation:

You should recognize that the given equation is in the point-slope form.

In order to find the y-intercept, rearrange the equation into slope-intercept form, y=mx+b .

$y-10=-20(x+\frac{1}{4})$

y-10=-20x-5

y=-20x+5

Since, b=5 , the y-intercept must be located at (0,5) .

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Example Question #1585 : Intermediate Geometry

True or false: The lines of the equations

2x+y = 12

and

x+2y = 12

have the same -intercept.

Possible Answers:

False

True

Correct answer:

False

Explanation:

The -intercept of a line is the point at which it intersects the -axis; its -coordinate at this point is 0, so its -coordinate can be found by substituting 0 for in the equation and solving for . Do this with both equations:

2x+y = 12

$2 \cdot 0 +y = 12$

0+ y = 12

y = 12

The -intercept of the line is at (0, 12) .

x+2y = 12

0+2y = 12

2y = 12

$\frac{2y }{2}= \frac{12}{2}$

y = 6

The -intercept of the line is at (0, 6) .

The two lines have different -intercepts.

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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1576 : Intermediate Geometry

Example Question #1577 : Intermediate Geometry

Example Question #1578 : Intermediate Geometry

Example Question #1571 : Intermediate Geometry

Example Question #1571 : Intermediate Geometry

Example Question #1581 : Intermediate Geometry

Example Question #1582 : Intermediate Geometry

Example Question #1583 : Intermediate Geometry

Example Question #1584 : Intermediate Geometry

Example Question #1585 : Intermediate Geometry

All Intermediate Geometry Resources

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