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Intermediate Geometry : x and y Intercept

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Example Question #1579 : 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, 32)

(0, 20)

(0, 18)

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 #1580 : Intermediate Geometry

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

Possible Answers:

(0, 18)

(0, 24)

(0, -17)

(0, 27)

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 #71 : X And Y Intercept

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

Possible Answers:

(0, -19)

(0, -1)

(0, -3)

(0, -13)

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 #72 : X And Y Intercept

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

Possible Answers:

(0, 16)

(0, 8)

(0, 24)

(0, 10)

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 #73 : X And Y Intercept

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

Possible Answers:

(0,-38)

(0, -29)

(0, 2)

(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 #74 : X And Y Intercept

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 #75 : X And Y Intercept

True or false: The lines of the equations

2x+y = 12

and

x+2y = 12

have the same -intercept.

Possible Answers:

True

False

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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Example Question #1581 : Intermediate Geometry

True or false: the lines of the equations

y = 6

and

x+ y = 6

have the same -intercept.

Possible Answers:

False

True

Correct answer:

True

Explanation:

The -intercept of a line is the point at which it intersects the -axis; its -coordinate at this point is 0.

The -coordinate of the line of the equation

x+ y = 6

can be found by substituting 0 for in the equation and solving for :

0+ y = 6

y=6

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

The line with equation y = b is a horizontal line with its -intercept at (0,b) , so the -intercept line of the equation y=6 has its -intercept at (0,6) as well.

Both lines indeed have the same -intercept.

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Example Question #1581 : Intermediate Geometry

True or false:

The lines of the equations

$y = \frac{2}{5}x+ 117$

and

$y = - \frac{5}{2}x+ 117$

have the same -intercept.

Possible Answers:

False

True

Correct answer:

True

Explanation:

Both equations are given in the slope-intercept form y = mx+b , in which the stand-alone constant is the -coordinate of the -intercept. In both equations, this value is 117, so (0, 117 ) is the -intercept of both equations.

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Example Question #78 : X And Y Intercept

Find the y-intercept of a line that has a slope of and passes through the point (12, 4) .

Possible Answers:

(0, -56)

(0,5)

(0, -14)

(0, 55)

Correct answer:

(0, -56)

Explanation:

Recall the point-slope form of the equation of a line that has a slope of and passes through the point (x_1, y_1) :

y-y_1=m(x-x_1)

Plug in the given point and the given slope.

y-4=5(x-12)

Rearrange the equation into slope-intercept form.

y-4=5x-60

y=5x-56

The y-intercept for this line is (0, -56) .

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Intermediate Geometry : x and y Intercept

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1579 : Intermediate Geometry

Example Question #1580 : Intermediate Geometry

Example Question #71 : X And Y Intercept

Example Question #72 : X And Y Intercept

Example Question #73 : X And Y Intercept

Example Question #74 : X And Y Intercept

Example Question #75 : X And Y Intercept

Example Question #1581 : Intermediate Geometry

Example Question #1581 : Intermediate Geometry

Example Question #78 : X And Y Intercept

All Intermediate Geometry Resources

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