Which of the following is an equation of the line that passes through the point (-2,3) and is perpendicular to the graph of the equation y = 3x - 2?

y = -1/3x + 7/3

Step-by-step explanation:

A line that is perpendicular to another line has the opposite reciprocal slope. That means we flip the slope of the original line and place a negative in front. Since the original slope is 3, the slope perpendicular is -1/3.

Now that we know the slope, and because they gave us a point on that line, we can create a line. Plug in the points and the slope into y = mx + b, to solve for b, the y-intercept.

3 = -1/3 (-2) + b

9/3 = 2/3 + b

7/3 = b

Now we can create a line in slope intercept form: y = -1/3x + 7/3

Here is Standard Form if needed: x + 3y = 7

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !