a m is the slope and it affects the direction and steepness of the incline or decline.
B
b b is the y-intercept and it affects where the line crosses the y-axis.
C
c See solution.
Practice makes perfect
a The variable m in the equation y=mx+b tells us the slope, or the rate of change, of the line. Slope can be written as:
m=change in y/change inx or m=rise/run.
This means that m tells us by how much the line will go up or down as we move to the right on the x-axis. If m is positive, our line goes up and to the right. If m is negative, our line goes down and to the right. Finally, the steepness of the line depends on whether m is a large number (rapid incline or decline) or a small number (gradual incline or decline).
b The variable b is the y-intercept and it affects where along the y-axis the line will cross. For example, if b=3, the line will cross the y-axis at (0,3) and if b=-2, the line will cross the y-axis at (0,-2).
c Let's look at the equation y=x-4 from Exploration 2. First we should graph this so that we can more easily compare it to the variations we will create.
Variations on m
Let's look at two different variations of the slope of our function. We can make the slope steeper by increasingm and we can change the direction of the line by makingm negative.
Variations on b
Now, let's look at two different variations of the y-intercept of our function. We can increase they-interceptb or we can decrease they-interceptb.
