X-intercept and y-intercept - GED Math

Card 0 of 90

Question

What is the x-intercept of the following equation?

Answer

The x-intercept is the value of when . Substitute the value for y.

Add one on both sides.

Divide by three on both sides.

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

The answer is: $\frac{1}{3}$

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Question

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

Answer

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.

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Question

Which of the following equations has as its graph a line with -intercept 9?

Answer

The equation in which when is graphed by a line that includes point - that is, its -intercept is 9. Therefore, substitute 0 for in each equation and solve for .

$9 \cdot 0 = y + 81$

$9 \cdot 0 + y = 81$

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

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Question

Find the and -intercepts of the following equation:

Answer

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 :

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Question

Find the and -intercepts for the following equation:

Answer

To find the , set the equal to 0:

Then solve for :

To find the , set the equal to 0:

Then solve for :

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Question

Find the and -intercepts for the following equation:

$y = x^{2} - 9$

Answer

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:

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Question

Given the following equation, what is the x-intercept?

Answer

The x-intercept is the value of when .

Substitute the value into the equation and solve for .

Subtract 6 on both sides.

Divide by 3 on both sides.

$\frac{-6}{3}= \frac{3x}{3}$

The answer is:

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Question

What is the y-intercept of the following equation?

Answer

The y-intercept is the value of when .

Substitute zero for x.

Subtract 1 on both sides.

Divide by 4 on both sides.

$\frac{4y }{4}=\frac{1}{4}$

The answer is: $\frac{1}{4}$

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Question

What is the y-intercept of the following line:

Answer

To find the y-intercept, we will look at the slope-intercept form of a line:

where m is the slope and b is the y-intercept.

So, given the equation

we can see the y-intercept is -11. Note that we must include the negative sign.

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Question

What is the y-intercept of the following equation?

Answer

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: $\frac{5}{2}$

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Question

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

Answer

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: $-\frac{1}{2}$

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Question

Determine the x-intercept of the following:

Answer

The x-intercept is the value of when .

Substitute into the given equation.

Add 6 on both sides.

Divide by 5 on both sides.

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

The answer is: $\frac{6}{5}$

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Question

What is the y-intercept given the following function? $y= \frac{1}{100}x$

Answer

The following equation is already written in slope-intercept form.

The y-intercept is the variable .

Since the value is absent, the y-intercept is zero.

The answer is:

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Question

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

Answer

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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Question

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?

Answer

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 .

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Question

Find the x-intercept of the following equation:

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

Answer

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

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Question

Find the x intercept of the following linear equation.

Answer

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.

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Question

Find the y intercept of the following linear equation.

Answer

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

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Question

What is the x-intercept of the following equation?

Answer

The x-intercept is the value of when . Substitute the value for y.

Add one on both sides.

Divide by three on both sides.

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

The answer is: $\frac{1}{3}$

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Question

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

Answer

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.

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