SAT Math - X-intercept and y-intercept

Find the y-intercept of the following line.

$\small 3$

$\small -12$

Explanation

To find the y-intercept of any line, we must get the equation into the form

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

To manipulate our equation into this form, we must solve for y. First, we must move the x term to the right side of our equation by subtracting it from both sides.

To isolate y, we now must divide each side by 3.

$\frac{3y}{3}=\frac{-4x}{3}-\frac{12}{3}$

$y=\frac{-4}{3}x-4$

Now that our equation is in the desired form, our y-intercept is simply

$\small b=-4$

Find the x-intercept of the following equation:

Explanation

In order to find the x-intercept, set y=0 then solve for x. For this equation that looks as follows:

$y=2x+6\rightarrow 0=2x+6$

Subtract 2x from both sides, then divide by -2 to get x by itself:

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

This gives a final answer of x=-3

What is the y-intercept of the following equation?

$\textup{The equation is not linear.}$

$-\frac{1}{2}$

Explanation

Rewrite the equation in slope-intercept form:

Our objective is to determine the value of , which represents the y-intercept.

Add two on both sides.

Divide by 2 on both sides.

$\frac{2y}{2}=\frac{ 2x+4}{2}$

The value of .

Find the x-intercept of the following equation:

Explanation

In order to find the x-intercept, set y=0 then solve for x. For this equation that looks as follows:

$2x+y=12\rightarrow 2x+0=12$

Divide by 2 to get x by itself:

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

This gives a final answer of x=6

Find the x-intercept of the following equation:

Explanation

In order to find the x-intercept, set y=0 then solve for x. For this equation that looks as follows:

$y=4x-16\rightarrow 0=4x-16$

Subtract 4x from both sides, then divide by -4 to get x by itself:

$\frac{-4x}{-4}=\frac{-16}{-4}$

This gives a final answer of x=4

What is the x-intercept of the equation ?

$\frac{2}{3}$

$\frac{3}{2}$

$-\frac{3}{2}$

Explanation

The x-intercept is the value of x when .

Add two on both sides, and then divide both sides by three.

The answer is: $\frac{2}{3}$

Define $h(x)=6- \log _{3}\left ( x-7 \right )$ .

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

The graph of has no -intercept.

Explanation

Evaluate :

$h(x)=6- \log _{3}\left ( x-7 \right )$

$h(0)=6- \log _{3}\left ( 0-7 \right )$

$h(0)=6- \log _{3}\left ( -7 \right )$

A negative number cannot have a logarithm, so is an undefined expression. Therefore, the graph of has no -intercept.

Define $f(x) = 2 \cdot 3^{x-4}- 7$

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

The graph of has no -intercept.

Explanation

Evaluate :

$f(x) = 2 \cdot 3^{x-4}- 7$

$f(0) = 2 \cdot 3^{0-4}- 7$

$= 2 \cdot 3^{-4}- 7$

$= 2 \cdot \frac{1}{81}- 7$

$= \frac{2}{81}- 7$

$=-6 \frac{79}{81} \approx -6.98$

What is the x-intercept and y-intercept of:

x-intercept= 4

y-intercept= -8

x-intercept=-8

y-intercept=4

x-intercept=2

y-intercept=-4

x-intercept = 1

y-intercept = -2

Explanation

The x-intercept is the value of x that will result in the y value equalling zero and the y-intercept is the y value that results when the x equals zero.

Therefore we replace x with zero to find the y-intecerpt.