Question

Write the equation for g (x)

Answer 1

Answer:

g(x) = (-1/25)x + (203/25)

Step-by-step explanation:

The general equation for a line is slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

We know that perpendicular lines have opposite-signed, reciprocal slopes of the original line. Therefore, if the slope of f(x) is m = 25, the slope of g(x) must be m = (-1/25).

To find the y-intercept, we can use the newfound slope and the values from the given point to isolate "b".

g(x) = mx + b                                    <----- General equation

g(x) = (-1/25)x + b                             <----- Plug (-1/25) in "m"

8 = (-1/25)(3) + b                               <----- Plug in "x" and "y" from point

8 = (-3/25) + b                                  <----- Multiply (1/25) and 3

200/25 = (-3/25) + b                       <----- Covert 8 to a fraction

203/25 = b                                      <----- Add (3/25) to both sides

Now that we know both the values of the slope and y-intercept, we can construct the equation of g(x).

g(x) = (-1/25)x + (203/25)