Answer:
A slope of zero means a horizontal line (parallel to the x axis). So the line is y=-6, which is the y intercept. There is no x term because y=-6 for all x.
Step-by-step explanation:
The average rate of change of f(x) on the interval [5, 5 + h] is 1
<h3>How to find the
average rate of change of f(x) on the interval [5, 5 + h]?</h3>
The equation of the function is given as:
f(x) = x + 11
The interval is given as: [5, 5 + h]
So, we start by calculating f(5) and f(5 + h)
This gives
f(5) = 5 + 11 = 16
f(5 + h) = 5 + h + 11 = h + 16
The average rate of change of f(x) on the interval [5, 5 + h] is then calculated as:
Rate = [f(5 + h) - f(5)]/[5 + h - 5]
Substitute the known values in the above equation
Rate = (h + 16 - 16)/(5 + h - 5)
Evaluate the sum and the difference
Rate = h/h
This gives
Rate = 1
Hence, the average rate of change of f(x) on the interval [5, 5 + h] is 1
Read more about the average rate of change at
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First you need to find the slope of the line containing those 2 points using the slope formula. Filling in with our info we have

. So the slope is -1.5. Now we need to find out the rest of the info, mainly the y-intercept. The line appears to go through the y axis at (0, 0), but let's make sure. We will use the slope we just found and one of our points to solve for the y-intercept. I picked point (4, -6). Filling in to solve for b we get -6 = (-1.5)(4) + b. Doing the multiplication on the right gives us -6=-6 + b. Add 6 to both sides to get that b = 0. Now let's use that and the slope we found to rewrite the equation in slope-intercept form. y = -1.5x + 0 or y = -1.5x and there you go!