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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #85 : Coordinate Geometry

$y=\frac{2}{3}x+12$

Find the -intercept.

Possible Answers:

x=-18

x=18

x=-8

x=-12

x=8

Correct answer:

x=-18

Explanation:

To find the -intercept, we set the -value equal to zero.

$y=\frac{2}{3}x+12$

$0=\frac{2}{3}x+12$

$-12=\frac{2}{3}x$

$\frac{3}{2}*-12=\frac{2}{3}x*\frac{3}{2}$

$\frac{3*-12}{2}=\frac{6}{6}x$

$\frac{-36}{2}=x$

-18=x

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Example Question #20 : How To Find X Or Y Intercept

What is the -intercept of $y=\frac{2}{3}x+12$ ?

Possible Answers:

Correct answer:

Explanation:

To find the -intercept, set the value equal to zero:

$y=\frac{2}{3}x+12$

$0=\frac{2}{3}x+12$

$-12=\frac{2}{3}x$

$\frac{3}{2}*-12=\frac{2}{3}x*\frac{3}{2}$

$\frac{3*-12}{2}=\frac{2*3}{3*2}x$

$\frac{-36}{2}=\frac{6}{6}x$

-18=x

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Example Question #21 : How To Find X Or Y Intercept

What is the y-intercept of the following line:

3x + 2y = 6 ?

Possible Answers:

(0, 2)

(2, 0)

(0, 3)

(0, -3)

(3, 0)

Correct answer:

(0, 3)

Explanation:

The y-intercept is precisely the point in which the x-value is . Thus, we plug in to our equation and solve for .

3(0) + 2y = 6

2y = 6

y = 3

Thus our intercept is (0,3) .

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Example Question #1471 : High School Math

What is the -intercept of the equation?

y=5x+5

Possible Answers:

(-1,0)

(25,0)

(5,0)

(-5,0)

(1,0)

Correct answer:

(-1,0)

Explanation:

To find the x-intercept of an equation, set the value equal to zero and solve for .

y=5x+5

0=5x+5

Subtract from both sides.

0-5=5x+5-5

-5=5x

Divide both sides by .

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

-1=x

Since the x-intercept is a point, we will write our answer in point notation: (-1,0) .

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Example Question #1472 : High School Math

Find the -intercept of -3x-5y=10 .

Possible Answers:

Correct answer:

Explanation:

Put the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

-3x-5y=10

-5y = 3x + 10

y = (-3/5)x + 10/(-5)

$y=-\frac{3}{5}x-2$

Now we can easily see that is the -intercept.

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Example Question #1473 : High School Math

A straight line passes through the points (1,3) and (2,2) .

What is the -intercept of this line?

Possible Answers:

(4,0)

(0,5)

(5,0)

(3,1)

(0,4)

Correct answer:

(4,0)

Explanation:

First calculate the slope:

$(\text{change in Y})/(\text{change in x}) = (1-2)/(3-2) = -1$

The standard equation for a line is Y=a*X + b .

In this equation, is the slope of the line, and is the -intercept. All points on the line must fit this equation. Plug in either point (1,3) or (2,2).

Plugging in (1,3) we get 3=-1*1 + b .

Therefore, b = 3 - (-1) =4 .

Our equation for the line is now:

Y= (-1)X + 4

To find the -intercept, we plug in y=0 :

0=(-1)x+4

x=4

Thus, the -intercept the point (4,0).

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Example Question #1474 : High School Math

Calculate the y-intercept of the line depicted by the equation below.

3x+6y=15

Possible Answers:

(0,6)

(5,0)

(0,2.5)

(0,5)

(2.5,0)

Correct answer:

(0,2.5)

Explanation:

To find the y-intercept, let equal 0.

3(0)+6y=15

We can then solve for the value of .

6y=15

$y=\frac{15}{6}=2.5$

The y-intercept will be (0,2.5) .

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Example Question #25 : Intercepts And Curves

What is the x-intercept of 2y=3x+5 ?

Possible Answers:

$-\frac{5}{3}$

$-\frac{10}{3}$

$\frac{3}{5}$

$-\frac{3}{5}$

$\frac{6}{5}$

Correct answer:

$-\frac{5}{3}$

Explanation:

To find the x-intercept, set y equal to zero and solve:

2y=3x+5

2(0)=3x+5

0=3x+5

Subtract from both sides:

-5=3x

Divide both sides by to isolate x:

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

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Example Question #26 : Intercepts And Curves

What is the y-intercept of the equation?

$y=\frac{2}{3}x+ 12$

Possible Answers:

(0,0)

(0,8)

(0,4)

(0,3)

(0,12)

Correct answer:

(0,12)

Explanation:

$y=\frac{2}{3}x+ 12$

To find the y-intercept, we set the value equal to zero and solve for the $\small y$ value.

$y= \frac{2}{3} (0) +12$

y=12

Since the y-intercept is a point, we will need to convert our answer to point notation.

(0,12)

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Example Question #1475 : High School Math

What line goes through points (-3,-7) and (2,3) ?

Possible Answers:

$y=\frac{1}{2}x-3$

$y=\frac{-1}{2}x+3$

y=2x-1

y=-2x-4

y=2x+5

Correct answer:

y=2x-1

Explanation:

First, we find the slope between the two points:

$P_{1}=(-3,-7)$ and $P_{2}=(2,3)$

$m= \frac{y_{2} - y_{1}}{x_{2}-x_{1}}=\frac{3-(-7)}{2-(-3)}=\frac{10}{5}=2$

Plug the slope and one point into the slope-intercept form to calculate the intercept:

y=mx+b

3=2(2)+b

b=-1

Thus the equation between the points becomes y=2x-1 .

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #85 : Coordinate Geometry

Example Question #20 : How To Find X Or Y Intercept

Example Question #21 : How To Find X Or Y Intercept

Example Question #1471 : High School Math

Example Question #1472 : High School Math

Example Question #1473 : High School Math

Example Question #1474 : High School Math

Example Question #25 : Intercepts And Curves

Example Question #26 : Intercepts And Curves

Example Question #1475 : High School Math

All High School Math Resources

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