Write the equation of a line that is perpendicular to the given line and that passes through the given point. y= 2/3x + 9; (–6, 5)

Hi!

The equation y = 2/3x + 9 is written in slope intercept, or y = mx + b. The m is the slope, and the b is the y intercept.

When a line is perpendicular to another, it meets it at a 90 degree angle. The slope of the line which is perpendicular to one with a given slope is the negative reciprocal of it, for example, if you had a line with slope 1/2, the slope of the line perpendicular to it would be -2.

So for this line, the negative reciprocal of 2/3 is -3/2. You now have one of the slots of the equation filled in, giving you:

y = -3/2x + b

Now, you just need to find b, as slope intercept leaves x and y as variables. Luckily, you are given a point that lays on the line; (-6, 5).

So to solve for b, you can substitute that point in, using -6 as x and 5 as y. That gives you:

5 = -3/2 (-6) + b

Now, just solve for b.

5 = -3/2 (-6) + b
5 = 9 + b
b = -4

And there's your solution for b, which you can fill in, giving you your final answer of:

y = -3/2x - 4

  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.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

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

the table tells us

g(-2) = 1g(1) = 31

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).