Slope-Intercept Form

I think the most useful form of straight-line equations is the “slope-intercept” form:

y = mx + b

This is called the slope-intercept form because

“m” is the direction of the line called the slope and

“b” gives the  starting point on the y axis called the y-intercept.

I like slope-intercept form the best. It is in the form “y=“, which makes it easiest to plug into, either for graphing or doing word problems. Just plug in your x-value; the equation is already solved for y.

But the best part about the slope-intercept form is that you can read off the slope and the intercept right from the equation. This is great for graphing.

y=5x+3

is an example of the Slope Intercept Form and represents the equation of a line with a starting point on the y axis at +3 and thedirection of the line is up 5 and right 1.

y= −2x + 6

represents the equation of a line with a starting point of +6 on the y axis and the direction of the line is 2 down and 1 to the right.

The easiest way to graph such a line, is to plot the starting point (called the y intercept)first. Then move the direction of the line (called the slope) in the form of a fraction, like rise over run, and from the y-intercept, count up (or down) for the rise, over (right ) for the run, and put the next point. Do it one more time. Then connect three points and this is your line.

A couple of examples might be helpful.

EXAMPLE :       y = 3x + 2
SOLUTION:
Starting point (y intercept) = 2 on the y axis ,  and then the direction (slope) =     
Start by graphing the y-intercept by going up 2 units on the y-axis.
From this point go UP (rise) another 3 units, then 1 unit to the RIGHT (run), and put another point. This is the second point. Connect the points and it should look like this:

EXAMPLE :      y = -3x + 2
SOLUTION:
Y-intercept = 2, slope = 
Start by graphing the y-intercept by going up 2 units on the y-axis.
From this point go DOWN (rise) 3 units, then 1 unit to the RIGHT (run), and put another point. This is the second point. Connect the points and it should look like this:

EXAMPLE :        y =    x + 2

SOLUTION:
Y-intercept = 2, slope =  
Start by graphing the y-intercept by going up 2 units on the y-axis.
From this point go UP (rise) another 3 units, then 5 unit to the RIGHT (run), and put another point. This is the second point. Connect the points and it should look like this:

 Credit- La Paz Intermediate School by Mr. Tellier