Question

A relation is plotted as a linear function on the coordinate plane starting at point C (0,−1)(0,−1) and ending at point D (2,−11)(2,−11) .

What is the rate of change for the linear function and what is its initial value?

the rate of change is ______ and the intivial value is______

Answer 1

To find the rate of change, or slope, pick two points. The slope, is change in y coordinates over change in x coordinates.
$slope = \frac{y2-y1}{x2-x1}$.

In this case, the slope is 
$\frac{-11+1}{2-0} = \frac{-10}{2} = -5$.
Remember that subtracting a negative number equals adding the number without the negative sign.
a-(-b) = a+b

Now for the y-intercept. The y-intercept is where the graph intersects the y-axis, where x = 0.
You have the coordinate (0, -1), where x = 0. So the y-intercept is -1.

Putting these values into the slope-intercept form y = mx+b, the equation is
y = -5x - 1