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

$\displaystyle 2y=12x+3\rightarrow 2y=0+3$

Divide both sides by 2 to get y by itself:

$\displaystyle \frac{2y}{2}=\frac{3}{2}$

This gives a final answer of y=3/2

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

$\displaystyle 3x-y=12\rightarrow 0-y=12$

Divide both sides by -1 to get y by itself:

$\displaystyle \frac{-1y}{-1}=\frac{12}{-1}$

This gives a final answer of y=-12

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

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

This gives a final answer of y=2

Rewrite the equation in slope-intercept form:

$\displaystyle y=mx+b$

Our objective is to determine the value of $\displaystyle b$, which represents the y-intercept.

Add two on both sides.

$\displaystyle 2y-2 +(2)= 2x+2+(2)$

$\displaystyle 2y= 2x+4$

Divide by 2 on both sides.

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

$\displaystyle y= x+2$

The value of $\displaystyle b =2$.

The y-intercept is the value of $\displaystyle y$ when $\displaystyle x=0$.

Substitute the value of $\displaystyle x=0$ into the given equation.

$\displaystyle y=2(2(0)-3)^2 = 2(0-3)^2 = 2(-3)^2 = 2(9)$

The answer is:  $\displaystyle 18$

The x-intercept is the value of x when $\displaystyle y=0$.

$\displaystyle 0= 3x-2$

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

$\displaystyle 0+2= 3x-2+2$

$\displaystyle 2=3x$

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

Evaluate $\displaystyle h(0)$:

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

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

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

A negative number cannot have a logarithm, so $\displaystyle h(0)$ is an undefined expression. Therefore, the graph of $\displaystyle h$ has no $\displaystyle y$-intercept.

For this problem we will need to use the slope equation:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

In our case $\displaystyle (x_1, y_1)=(-1,0)$ and $\displaystyle (x_2, y_2)=(3,5)$

Therefore, our slope equation would read:

$\displaystyle m=\frac{5-0}{3--1}=\frac{5}{4}$

To find the slope of this function we first need to get it into slope-intercept form

$\displaystyle y=mx+b$ where $\displaystyle m=slope$

To do this we need to divide the function by 3:

$\displaystyle 3y=6x-12$

$\displaystyle y=2x-4$

From here we can see our m, which is our slope equals 2

To find the slope for the line that has these points we will use the slope formula with two of the points.

In our case $\displaystyle (x_1, y_1)= (1,5)$ and $\displaystyle (x_2, y_2)=(2, 8)$

Now we can use the slope formula:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{8-5}{2-1}=\frac{3}{1}=3$