Write an equation of the line that passes through
(3, 5) and is perpendicular to the graph of y = –3x +7. write your final equation in slope-intercept form.

y = 1/3 x + 4

Step-by-step explanation:

The slopes of perpendicular lines are negative reciprocals. The given line is

y = -3x + 7

which is already in the slope-intercept form, y = mx + b, where m is the slope.

The slope of the given line is -3.

The slope of the perpendicular is the negative reciprocal of -3 which is 1/3.

The line we are looking for has an equation of the form

y = 1/3x + b

We need to find b. We use the x- and y-coordinates of the given point as x and y in the equation above, and we solve for b.

y = 1/3x + b

5 = (1/3)(3) + b

5 = 1 + b

4 = b

Now that we know that b = 4, we replace b with 4 in the equation

y = 1/3x + b to get the answer.

y = 1/3 x + 4

10 miles

step-by-step explanation: