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Intermediate Geometry : Coordinate Geometry

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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 #301 : Coordinate 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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Example Question #81 : X And Y Intercept

Give the -coordinate of the -intercept of the line of the equation

8x + 7y = 43

Possible Answers:

$5\frac{3}{8}$

$-\frac{7}{8}$

$6\frac{1}{7}$

$-1\frac{1}{7}$

Correct answer:

$5\frac{3}{8}$

Explanation:

The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by substituting 0 for in the equation and solving for :

8x + 7y = 43

8x + 7 (0) = 43

8x +0= 43

8x = 43

Divide both sides by 8:

$\frac{8x }{8}= \frac{43}{8}$

$x= 5\frac{3}{8}$

The -intercept of the graph is at the point $\left ( 5\frac{3}{8} , 0\right )$ .

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Example Question #82 : X And Y Intercept

Give the -coordinate of the -intercept of the line of the equation

8x + 7y = 43

Possible Answers:

$5\frac{3}{8}$

$6\frac{1}{7}$

$-\frac{7}{8}$

$-1\frac{1}{7}$

Correct answer:

$6\frac{1}{7}$

Explanation:

The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by substituting 0 for in the equation and solving for :

8x + 7y = 43

8 (0) + 7y = 43

0+ 7y = 43

7y = 43

Divide both sides by 7:

$\frac{7y }{7}= \frac{43}{7}$

$y = 6\frac{1}{7}$

The -intercept of the graph is at the point $\left (0, 6\frac{1}{7} \right )$ .

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Example Question #1 : How To Find The Equation Of A Curve

If a line's -intercept is . and the -intercept is , what is the equation of the line?

Possible Answers:

5x-y=-1

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

-5x+y=-1

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

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

Correct answer:

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

Explanation:

Write the equation in slope-intercept form:

y=mx+b

We were given the -intercept, , which means b=-1 :

y=mx-1

Given the -intercept is , the point existing on the line is (5,0) . Substitute this point into the slope-intercept equation and then solve for to find the slope:

0=m(5)-1

Add to each side of the equation:

1=5m

Divide each side of the equation by :

$m=\frac{1}{5}$

Substituting the value of back into the slope-intercept equation, we get:

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

By subtracting $-\frac{1}{5}x$ on both sides, we can rearrange the equation to put it into standard form:

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

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Example Question #2 : How To Find The Equation Of A Curve

Find the -intercept of:

y=4x+2

Possible Answers:

x=2

x=-2

x=-0.5

x=0.5

x=1

Correct answer:

x=-0.5

Explanation:

To find the x-intercept, we need to find the value of when y=0 .

So we first set to zero.

y=4x+2

turns into

0=4x+2

Lets subtract from both sides to move to one side of the equation.

-4x=4x-4x+2

After doing the arithmetic, we have

-4x=2 .

Divide by from both sides

$\frac{-4x}{-4}=\frac{2}{-4}$

x=-0.5

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Example Question #1 : How To Find The Equation Of A Curve

What is the -intercept of:

y=x^2+x+9

Possible Answers:

y=10

y=-9

x=9

y=9

x=2

Correct answer:

y=9

Explanation:

To find the y-intercept, we set x=0

y=x^2+x+9

turns into

y=0^2+0+9 .

After doing the arithmetic we get

y=9 .

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Example Question #1 : How To Find The Equation Of A Curve

What is the -intercept of:

y=3x+3

Possible Answers:

x=1

y=-1

x=0

x=-1

y=1

Correct answer:

x=-1

Explanation:

The x-intercept can be found where y=0

y=3x+3

turns into

0=3x+3 .

Lets subtract from both sides to solve for .

-3x=3x-3x+3

After doing the arithmetic we have

-3x=3 .

Divide both sides by

$\frac{-3x}{-3}=\frac{3}{-3}$

x=-1

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Example Question #5 : How To Find The Equation Of A Curve

Suppose two intercepts create a line. If the -intercept is and -intercept is , what is the equation of the line?

Possible Answers:

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

x-2y=0

y=-2x+2

y=2x+2

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

Correct answer:

y=-2x+2

Explanation:

Rewrite the intercepts in terms of points.

X-intercept of 1: (1,0) .

Y-intercept of 2: (0,2)

Write the slope-intercept form for linear equations.

y=mx+b

Substititute the y-intercept into the slope-intercept equation.

2=m(0)+b

b=2

Substitute both the x-intercept point and the y-intercept into the equation to solve for slope.

0=m(1)+2

-2=m

Rewrite by substituting the values of and into the y-intercept form.

y=-2x+2

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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1581 : Intermediate Geometry

Example Question #301 : Coordinate Geometry

Example Question #78 : X And Y Intercept

Example Question #81 : X And Y Intercept

Example Question #82 : X And Y Intercept

Example Question #1 : How To Find The Equation Of A Curve

Example Question #2 : How To Find The Equation Of A Curve

Example Question #1 : How To Find The Equation Of A Curve

Example Question #1 : How To Find The Equation Of A Curve

Example Question #5 : How To Find The Equation Of A Curve

All Intermediate Geometry Resources

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