College Algebra

Question

Find the equation of the linear function g that has g(2)=8 and that is perpendicular to m(a)=8/7a+33

Answer 1

Hello, thank you for taking the time to post your question!

Because the function here is perpendicular that means that the slop will be the opposite reciprocal, so m = -7/8

From there then we can plug in the slope and the point (2, 8) to figure out what the corresponding y-intercept is for this scenario

8 = -7/8(2) + b

8 = -14/8 + b

8 + 14/8 = b

b = 39/4

putting it all together then the equation of the line here is

y = -7/8x + 39/4

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

If m(a)=8/7a+33 then the slope of that line is 8/7. The slope of a line perpendicular to that will be -7/8 so:

g(x) = -7/8x + b

But it is given that g(2)=8 so 8 = -7/8(2) + b solving for b, you get: b = 39/4 so:

g(x) = -7/8x + 39/4