Part 6 Passes through (-6, 10) & (-3, -2)
Slope:
Y-Intercept:
Equation of the line:


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SLOPE

To find the slope, you divide the difference of the y values by the difference in the x values.

10-(-2)=10+2=12

-6-(-3)=-6+3=-3

12/-3=-4

So, our slope is -4.

Y- INTERCEPT

To find the y-intercept, we plug our slope and one of our points into the slope intercept equation (y=mx+b) and solve for b, which is the y-intercept. We will use the point (-6,10).

10=-4(-6)+b

Flip the equation so b is on the left.

-4(-6)+b=10

24+b=10

Subtract 24 from both sides.

b=-14

Our y-intercept is -14.

EQUATION

The slope intercept equation is y=mx+b, where m is the slope and b is the y-intercept. Therefore, we have the following answers.

Slope: -4

y-Intercept: -14

Equation of the Line: y=-4x-14

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  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).