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:

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

For this question we need to get the function into slope intercept form first which is

\(\displaystyle y=mx+b\) where the m equals our slope.

In our case we need to do algebraic opperations to get it into the desired form

\(\displaystyle 2y-3=8x+13\)

\(\displaystyle 2y=8x+16\)

\(\displaystyle y=\frac{8x+16}{2}\)

\(\displaystyle y=4x+8\)

Therefore our slope is 4

To find the slope for a given equation, it needs to first be put into the "y=mx+b" format. Then our slope is the number in front of the x, or the "m". For this equation this looks as follows:

First subtract 2x from both sides:

\(\displaystyle 2x+3y=6\)

\(\displaystyle -2x\)                \(\displaystyle -2x\)

That gives us the following:

\(\displaystyle 3y=-2x+6\)

Divide all three terms by three to get "y" by itself:

\(\displaystyle \frac{3y}{3}=\frac{-2x}{3}+\frac{6}{3}\rightarrow y=\frac{-2x}{3}+2\)

This means our "m" is -2/3

To find the slope for a given equation, it needs to first be put into the "y=mx+b" format. Then our slope is the number in front of the x, or the "m". For this equation this looks as follows:

First add x to both sides:

\(\displaystyle 4y-x=7\)

\(\displaystyle +x\)                \(\displaystyle +x\)

That gives us the following:

\(\displaystyle 4y=x+7\)

Divide all three terms by four to get "y" by itself:

\(\displaystyle \frac{4y}{4}=\frac{x}{4}+\frac{7}{3}\rightarrow y=\frac{x}{4}+\frac{7}{4}\)

This means our "m" is 1/4

To find the slope for a given equation, it needs to first be put into the "y=mx+b" format. Then our slope is the number in front of the x, or the "m". For this equation this looks as follows:

\(\displaystyle y=6x+3\)

Our equation is already in the "y=mx+b" format, so our "m" is 6.

To find the slope for a given equation, it needs to first be put into the "y=mx+b" format. Then our slope is the number in front of the x, or the "m". For this equation this looks as follows:

\(\displaystyle y=6-2x\)

To put our equation in the "y=mx+b" format, flip the two terms on the right side of the equation:

\(\displaystyle y=-2x+6\)

So our "m" in this case is -2.

Subtract \(\displaystyle 7y\) on both sides.

\(\displaystyle y-7y=-7x+7y-7y\)

Simplify both sides.

\(\displaystyle -6y = -7x\)

Divide by negative 6 on both sides.

\(\displaystyle \frac{-6y }{-6}= \frac{-7x}{-6}\)

\(\displaystyle y=\frac{7}{6}x\)

The slope is:  \(\displaystyle \frac{7}{6}\)

To determine the slope, we need the equation in slope intercept form.

\(\displaystyle y=mx+b\)

Multiply by four on both sides to eliminate the fraction.

\(\displaystyle \frac{1}{4}y \cdot 4=4 (2x-2y)\)

\(\displaystyle y= 8x-8y\)

Add \(\displaystyle 8y\) on both sides.

\(\displaystyle y+8y= 8x-8y+8y\)

Combine like-terms.

\(\displaystyle 9y = 8x\)

Divide by nine on both sides.

\(\displaystyle \frac{9y }{9}= \frac{8x}{9}\)

\(\displaystyle y=\frac{8}{9}x\)

The value of \(\displaystyle m\), or the slope, is \(\displaystyle \frac{8}{9}\).