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 $\displaystyle m=5$.

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

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

In this case $\displaystyle m=44$

First flip the sign $\displaystyle m=-44$

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

Do this to make the slope 

$\displaystyle m=-\frac{1}{44}$

The slope of the perpendicular line is

$\displaystyle m=-\frac{1}{44}$.

To be able to identify the slope of a line, we need to get it in the form of 

$\displaystyle y=mx+b$.

To do this we need to change the coefficient of y to be $\displaystyle 1$ instead of $\displaystyle 2$. To do this, divide both sides of the equation by $\displaystyle 2$.

$\displaystyle y=\frac{3}{2}x+2$

Now we can tell what the value of m, or the slope, is: $\displaystyle \frac{3}{2}$

The slope of the line is determined by $\displaystyle \frac{rise}{run}$. In other words, we can use the formula $\displaystyle \frac{y_2-y_1}{x_2-x_1}$.

Let's choose the coordinate $\displaystyle (3,5)$ to be ($\displaystyle x_1$ , $\displaystyle y_1$)  and $\displaystyle (4,7)$ to be ($\displaystyle x_2$ , $\displaystyle y_2$).

We can now use the formula above:

$\displaystyle \frac{7-5}{4-3}=2$

The formula to calculate slope  between two points in a line is $\displaystyle m=\frac{Y-y}{X-x}$, for points $\displaystyle (X,Y)$ and $\displaystyle (x,y)$. 

If we pick $\displaystyle (1,12)$ as our $\displaystyle (X,Y)$ and $\displaystyle (-7, 8)$ as our $\displaystyle (x,y)$, then:

$\displaystyle m = \frac{12-8}{1-(-7)}$
This simplifies to $\displaystyle m=\frac{4}{8}$, which can be reduced to  $\displaystyle m=\frac{1}{2}$

The slope-intercept form of a line is $\displaystyle y=mx+b$.

It is known that parallel lines have the same slope and therefore a line that is parallel to:

$\displaystyle y=14x+7$

MUST have the same slope of $\displaystyle 14$.