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 $\displaystyle \frac{8}{9}$.

Write the slope equation.

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

Substitute the points and solve for the slope.

$\displaystyle m=\frac{3-8}{-1-3} = \frac{-5}{-4}$

The answer is:  $\displaystyle \frac{5}{4}$

The polynomial is in standard form of a parabola.

$\displaystyle y=ax^2+bx+c$

To determine the vertex, first write the formula.

$\displaystyle x=-\frac{b}{2a}$

Substitute the coefficients.

$\displaystyle x=-\frac{-5}{2(-3)} = -\frac{5}{6}$

Since the $\displaystyle a$ is negative is negative, the parabola opens down, and we will have a maximum.

The answer is:  $\displaystyle -\frac{5}{6}, \textup{Max}$

The parabola is in the form:  $\displaystyle y=ax^2+bx+c$

$\displaystyle y=-3x^2+4x$

The vertex formula will determine the x-value of the max or min.  Since the value of $\displaystyle a$ is negative, the parabola will open downward, and there will be a maximum.

Write the vertex formula and substitute the correct coefficients.

$\displaystyle x=-\frac{b}{2a} = -\frac{4}{2(-3)} = \frac{2}{3}$

Substitute this value back in the parabolic equation to determine the y-value.

$\displaystyle y=-3( \frac{2}{3})^2+4( \frac{2}{3}) = \frac{4}{3}$

The answer is:  $\displaystyle \textup{Max}, (\frac{2}{3}, \frac{4}{3})$