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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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Example Question #58 : X And Y Intercept

Given the following table of a linear function, find the y-intercept.

x	f(x)
-3	-6
-1	4
2	19
4	29

Possible Answers:

Correct answer:

Explanation:

Start by taking a pair of points and find the slope of the line.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{4-(-6)}{-1-(-3)}=\frac{10}{2}=5$

Next, re-write the equation in point-slope form.

y-(-6)=5(x-(-3))

Rewrite this equation so that it is in slope-intercept form.

y+6=5(x+3)

y+6=5x+15

y=5x+9

The y-intercept for this line is .

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Example Question #59 : X And Y Intercept

Find the y-intercept of a line that has a slope of and goes through the point (8, 1) .

Possible Answers:

(0, -5)

(0, 33)

(0, 26)

(0, 14)

Correct answer:

(0, 33)

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-1=-4(x-8)

Rearrange the equation into slope-intercept form.

y-1=-4x+32

y=-4x+33

The y-intercept for this line is (0, 33) .

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Example Question #60 : X And Y Intercept

Find the y-intercept of a line that goes through the point (9, 9) and has a slope of .

Possible Answers:

(0, 9)

(0, 19)

(0, 87)

(0, -126)

Correct answer:

(0, -126)

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-9=15(x-9)

Rearrange the equation into slope-intercept form.

y-9=15x-135

y=15x-126

The y-intercept for this line is (0, -126) .

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Example Question #61 : X And Y Intercept

Find the y-intercept of a line that has a slope of and passes through the point (-5, 6) .

Possible Answers:

(0, 51)

(0, 10)

(0, -26)

(0, 46)

Correct answer:

(0, 46)

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-6=8(x+5)

Rearrange the equation into slope-intercept form.

y-6=8x+40

y=8x+46

The y-intercept for this line is (0, 46) .

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Example Question #62 : X And Y Intercept

Find the y-intercept of the line that has a slope of and passes through the point (-7, 14) .

Possible Answers:

(0, 2)

(0, -12)

(0, 9)

(0, -7)

Correct answer:

(0, -7)

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-14=-3(x+7)

Rearrange the equation into slope-intercept form.

y-14=-3x-21

y=3x-7

The y-intercept for this line is (0, -7) .

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Example Question #1571 : Intermediate Geometry

Find the y-intercept of the line that passes through the point (8, 0) and has a slope of .

Possible Answers:

(0, -30)

(0, 40)

(0, -100)

(0, 80)

Correct answer:

(0, 80)

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=-10(x-8)

Rearrange the equation into slope-intercept form.

y=-10x+80

The y-intercept for this line is (0, 80) .

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Example Question #1572 : Intermediate Geometry

Find the y-intercept of the line that has a slope of and passes through the point (-15, -10) .

Possible Answers:

(0, 120)

(0, 170)

(0, 150)

(0, 140)

Correct answer:

(0, 170)

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+10=12(x+15)

Rearrange the equation into slope-intercept form.

y+10=12x+180

y=12x+170

The y-intercept for this line is (0, 170) .

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Example Question #1573 : Intermediate Geometry

What is the y-intercept of the line with the equation y-3=9(x-1) ?

Possible Answers:

(0, -1)

(0, -9)

(0, -6)

(0, 3)

Correct answer:

(0, -6)

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-3=9(x-1)

y-3=9x-9

y=9x-6

Since, b=-6 , the y-intercept must be located at (0, -6)

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Example Question #1574 : Intermediate Geometry

What is the y-intercept of a line with the equation y+1=-2(x-4) ?

Possible Answers:

(0, 5)

(0, -4)

(0, 7)

(0, -1)

Correct answer:

(0, 7)

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+1=-2(x-4)

y+1=-2x+8

y=-2x+7

Since, b=7 , the y-intercept must be located at (0,7)

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Example Question #1575 : Intermediate Geometry

What is the y-intercept of a line that has the equation $y+9=\frac{1}{2}(x+4)$ ?

Possible Answers:

(0, -2)

(0, -9)

(0, -5)

(0, -7)

Correct answer:

(0, -7)

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 .

$y+9=\frac{1}{2}(x+4)$

$y+9=\frac{1}{2}x+2$

$y=\frac{1}{2}x-7$

Since, b=-7 , the y-intercept must be located at (0,-7)

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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #58 : X And Y Intercept

Example Question #59 : X And Y Intercept

Example Question #60 : X And Y Intercept

Example Question #61 : X And Y Intercept

Example Question #62 : X And Y Intercept

Example Question #1571 : Intermediate Geometry

Example Question #1572 : Intermediate Geometry

Example Question #1573 : Intermediate Geometry

Example Question #1574 : Intermediate Geometry

Example Question #1575 : Intermediate Geometry

All Intermediate Geometry Resources

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