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 $\displaystyle m=13$.

To find the slope of a line with two points you must properly plug the points into the slope equation for two points which is

$\displaystyle m=\frac{Y-y}{X-x}$

We must then properly assign the points to the equation as $\displaystyle (X,Y)$ and $\displaystyle (x,y)$.

In this case we will make $\displaystyle (9,-7)$ our  and $\displaystyle (8,12)$ our .

Plugging the points into the equation yields 

$\displaystyle m=\frac{-7-12}{9-8}$

Perform the math to arrive at 

$\displaystyle m=\frac{-19}{1}$

The answer is $\displaystyle m=-19$.

In the standard form of a line $\displaystyle y=mx+b$ the slope is represented by the variable $\displaystyle m$.

In this case the line $\displaystyle y=15x+13$ has a slope of $\displaystyle 15$.

The answer is $\displaystyle 15$.

The equation of the line is written in slope-intercept form, $\displaystyle y=mx+b$, where $\displaystyle m$ is the slope and $\displaystyle b$ is the y-intercept. In this example, the y-intercept is a negative number.

$\displaystyle y=4x-7$

$\displaystyle m=4$

$\displaystyle b=-7$

The y-intercept is the point at which the line intersects the y-axis.

It does this at .

We plug  in for  in our equation, $\displaystyle y=16x+91$, to give us $\displaystyle y=16(0)+91$.

Anything multiplied by  is , so $\displaystyle y=91$.

Our coordinates for the y-intercept are $\displaystyle (0,91)$.

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 $\displaystyle m=16$.

To find the slope of a line with two points you must properly plug the points into the slope equation for two points which looks like

We must then properly assign the points to the equation as  and .

In this case we will make $\displaystyle (8,16)$ our  and $\displaystyle (4,8)$ our .

Plugging the points into the equation yields 

$\displaystyle m=\frac{(16-8)}{(8-4)}$

Perform the math to arrive at 

$\displaystyle m=\frac{8}{4}$

The answer is $\displaystyle m=2$.

To find the slope of a line with two points you must properly plug the points into the slope equation for two points which looks like

We must then properly assign the points to the equation as  and .

In this case we will make $\displaystyle (2,10)$ our , and $\displaystyle (1,5)$ our .

Plugging the points into the equation yields 

$\displaystyle m=\frac{10-5}{2-1}$

Perform the math to arrive at 

$\displaystyle m=\frac{5}{1}$

The answer is $\displaystyle m=5$.