Transcript Slope-Intercept Form and Direct Variations

 Slope-intercept form
represents a linear function
and is given by: y=mx+b,
where m is the slope, b is
the y-intercept, and y and x
are the output and input,
respectively.
Let’s look at calculating
the slope of two quantities
x and y, which share a
direct variation and then
writing this relationship in
slope-intercept form.
If two quantities share a direct
variation, then the ratio
between the quantities must
be constant.
Solving this equation for y, we
get the following.
In this form k represents slope,
which happens to be constant.
Also, notice that this is a special
case of the slope-intercept form.
Slope-intercept form is given by the
following.
If the y-intercept happens to be 0,
this equation matches the equation
shown earlier for a direct variation.
Substitute in
value for b and
simplify.
m and k both
represent slope.