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:

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