In the standard form of a line  the slope is represented by the variable .

In this case the line $\displaystyle y=5x-32$ has a slope of $\displaystyle 5$.

The answer is $\displaystyle 5$.

In the slope-intercept form of a line, , the y-intercept when the line intersects the y-axis.

It does this at $\displaystyle x=0$.

So we plug $\displaystyle 0$ in for $\displaystyle x$ in our equation $\displaystyle y=4x+15$ to give us $\displaystyle y=4(0)+15$.

Anything multiplied by $\displaystyle 0$ is $\displaystyle 0$ so $\displaystyle y=15$.

Our coordinates for the y-intercept are $\displaystyle (0,15)$.

In the standard form of a line  the y-intercept occurs when the line intersects the y-axis.

It does this at 

So we plug  in for  in our equation $\displaystyle y=9x-17$ to give us $\displaystyle y=9(0)-17$.

Anything multiplied by  is  so $\displaystyle -17$.

Our coordinates for the y-intercept are $\displaystyle (0,-17)$.

Parallel lines have the same slope.

If an equation is in point-slope form, $\displaystyle y=mx+b$, we take the $\displaystyle m$ from our equation and set it equal to the slope of our parallel line.

In this case $\displaystyle m=5$

The slope of our parallel line is $\displaystyle 5$.

The point resides in quadrant I (the upper right quadrant), so both values must both be positive. The only possible solution is $\displaystyle \small (3,5)$.

The slope of a perpendicular lines has the negative reciprocal of the slope of the original line.

If an equation is in point-slope form, , we use the  from our equation as our original slope.

In this case $\displaystyle m=-15$

First flip the sign to get $\displaystyle m=15$. 

To find the reciprocal you take the integer and make it a fraction by placing a $\displaystyle 1$ over it. If it is already a fraction just flip the numerator and denominator.

Do this to make the slope $\displaystyle m=\frac{1}{15}$

The slope of the perpendicular line is $\displaystyle \frac{1}{15}$.

In the standard form equation of a line, , the slope is represented by the variable .

In this case the line $\displaystyle y=13x+17$ has a slope of $\displaystyle 13$.

Therefore the answer is $\displaystyle m=13$.

In the slope-intercept form of a line, , the slope is represented by the variable .

In this case the line

has a slope of .

The answer is $\displaystyle m=15$.

In the slope-intercept form of a line, , the y-intercept is when the line intersects the y-axis.

It does this at .

So we plug  in for  in our equation

$\displaystyle y=31x-65$ 

to give us

$\displaystyle y=31(0)-65$

Anything multiplied by  is  so

$\displaystyle y=-65$

Our coordinates for the y-intercept are $\displaystyle (0,-65)$.

Parallel lines have the same slope.

If an equation is in slope-intercept form, , we take the  from our equation and set it equal to the slope of our parallel line.

In this case $\displaystyle m=16$.

The slope of our parallel line is $\displaystyle m=16$.