Question 24077
Compare the slope-intercept form of a linear equation with an equation for direct variation.

Slope-intercept form:
{{{y = mx + b}}} m is the slope of the line.
Direct variation:
{{{y = kx}}} y varies diectly as x. k is the constant of variation.

Do you see the similarity?

Let's compare the two equations using numbers:

Slope-intercept:
{{{y = 4x+3}}} The slope (m) is 4 and the y-intercept (b) is 3.

Direct variation:
{{{y = kx}}} To find the value of k, you'll need to know the values of y and x.  Let's say that y = 8 when x = 2, so that k = y/x = 8/2 = 4.  So you can write:
{{{y = 4x}}}

Now let's graph these two lines and compare them.
{{{graph(300,200,-5,5,-5,5,4x+3,4x)}}}
The red line is: {{{y = 4x+3}}}
The green line is: {{{y = 4x}}}

Conclusion:
The constant of variation in a direct-variation equation is the slope of the line when the equation is graphed.