SOLUTION: What do you do to the equation y=x to make its graph steeper? What do you do to make the graph for y=x flatter?

Question 112470: What do you do to the equation y=x to make its graph steeper?
What do you do to make the graph for y=x flatter?

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given the equation:
.
y = x
.
This equation is in the slope intercept form of y = mx + b where m (the multiplier of x) is the
slope of the line, and b is the value on the y-axis where the line crosses.
.
For the given equation the multiplier of x is +1. [b is zero, so the line goes through the
origin where y is equal to zero.]
.
So we know that the slope of the line of the given equation is +1. To make this line steeper,
all you have to do is to increase the slope. As a result you can say that:
.
y = 2x
.
is steeper than the line defined by the equation y = x. And y = 5x is even steeper than
y = 2x. And y = 10x is even steeper than y = 5x.
.
In the other direction, if you want the original line to slope less than y = x, all you need
to do is make the slope less than 1, but greater than 0. The smaller the fraction, the
more the slope comes closer and closer to being a horizontal line.
.
So
.
y = (3/4)x
.
is less steep than y = x. Even less steep would be y = (1/2)x. And y = (1/4)x is less steep
yet.
.
Hope this helps you to understand the problem a little better.
.

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