Find the linear function f(x) that satisfies f(-2) = -5, and has a graph that is perpendicular to the line -27x-9y=4

Question

Find the linear function  f(x) that satisfies  f(-2) = -5, and has a graph that is perpendicular to the line -27x-9y=4

tyteen4a03 · Answer

Turn -27x-9y=4 into the slope-intercept form, you get y = (-27/9)x - 4. This means the slope of -27x-9y=4 would be (-27/9) = -3.
From f(-2) = -5, we know that when x = -2, y would be -5. This means this new line passes through (-2, -5).
We also know that the product of slope of 2 perpendicular lines would be -1. Let the slope of the new line be m, we have -3m = -1. Solve it, and you get 1/3.
Now we put the information together again with the point-slope form, we have $y + 5 = (1/3)(x + 2)$. Turn them into the general form, and you get -x + 3y + 13 = 0.

anonymous · Answer

thank you