X-intercept and y-intercept

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GED Math › X-intercept and y-intercept

Questions 1 - 10

1

What is the y-intercept of the following equation?

$\frac{5}{2}$

$\frac{2}{5}$

$\frac{5}{3}$

$\frac{3}{2}$

Explanation

The y-intercept is the value of when .

Substitute into the equation.

Divide by 2 on both sides.

$\frac{2y}{2}=\frac{5}{2}$

The answer is: $\frac{5}{2}$

2

Find the and -intercepts for the following equation:

$y = x^{2} - 9$

Explanation

To find the , set equal to 0:

$0 = x^{2} - 9$

Then solve:

$9 = x^{2}$

$\sqrt{9} = \sqrt{x^{2}}$

Remember, the square root of is both and

To find the, set equal to 0:

$y = 0^{2} - 9$

Then solve:

3

Find the and -intercepts of the following equation:

Explanation

To find the , we need to set equal to 0 in our equation:

Now solve for :

To find the , we need to set equal to 0 in our equation:

Now solve for :

4

If the x-intercept is 4, and the y-intercept is 2, what must be the slope?

$-\frac{1}{2}$

$\frac{1}{2}$

$\frac{1}{8}$

$-\frac{1}{8}$

Explanation

We can obtain two known points from using the intercepts. The y-intercept is when , and x-intercept is when .

The points are:

Write the formula for the slope.

$m= \frac{y_2-y_1}{x_2-x_1} = \frac{0-2}{4-0} = -\frac{2}{4}$

The answer is: $-\frac{1}{2}$

5

Which of the following equations has as its graph a line with -intercept ?

Explanation

The equation in which when is graphed by a line that includes point - that is, its -intercept is . Therefore, substitute 0 for in each equation and solve for .

$9 \cdot 0 = x + 81$

$x + 9 \cdot 0 = 81$

The correct choice is , since is a solution of this equation.

6

Find the y intercept of the following linear equation.

$\frac{2}{3}$

$\frac{6}{7}$

$-\frac{1}{2}$

Explanation

Find the y intercept of the following linear equation.

The y-intercept occurs when x is 0. Find it by plugging in 0 for x and solving for y.

$4y=12(0)+6 \rightarrow 4y=6$

$4y=6\rightarrow y=\frac{6}{4}=\frac{3}{2}=1.5$

So our answer is 1.5

7

Find the x intercept of the following linear equation.

$-\frac{1}{2}$

$\frac{1}{2}$

Explanation

Find the x intercept of the following linear equation.

x intercepts occur when y=0, in other words, when we have no height.

So, plug in 0 for y and solve for x

$4(0)=12x+6 \rightarrow 0=12x+6$

$0=12x+6 \rightarrow -6=12x$

$x=-\frac{6}{12}=-\frac{1}{2}$

So our x intercept is negative one half.

8

Find the x-intercept of the following equation:

$\large y-5=2x+12$

Explanation

Find the x-intercept of the following equation:

$\large y-5=2x+12$

The x-intercept is the point where the line crosses the x-axis. At this point, the y-value must be 0.

To find the x-intercept, plug in "0" for y and solve for x.

$0-5=2x+12\rightarrow-5=2x+12$

$-5=2x+12\rightarrow-5-12=2x\rightarrow-17=2x$

Now finish up by dividing by 2:

$x=-\frac{17}{2}=-8.5$

We can check our answer by plugging it back into our equation:

Everything looks good, so our answer is -8.5

9

The following points lie on a line.

$\begin{tabular}{ |c|c| } \hline x& y \ \hline -3 & 11 \ 1 & -1 \ 3 &-7\ \hline \end{tabular}$

What is the equation of the line?

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

Explanation

Start by finding the slope of the line by using any two points.

Recall how to find the slope of a line:

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

Using the points $(1, -1)\text{ and }(3, -7)$ , we can find the slope.

$\text{Slope}=\frac{-7-(-1)}{3-1}=\frac{-6}{2}=-3$

Now, we can write the following equation:

To find the value of , the y-intercept, plug in any point into the equation above. Using the point , we can write the following equation:

Thus, the complete equation for this line is .

10

Find the x-intercept of the line with the equation .

$(\frac{6}{5}, 0)$

$(-\frac{3}{5}, 0)$

Explanation

Recall that at the x-intercept, the y-coordinate will be . Thus, plug in for in the given equation.

$x=\frac{6}{5}$

The coordinates of the x-intercept is located at $(\frac{6}{5}, 0)$ .

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