Write the equation of a line in slope-intercept form that is perpendicular to the line y=3/5x-1 and passes through the point (-9, 4).

Given:

(-9, 4)

x1 = -9 

y1 =4

Perpendicular to the line: y =3/5x -1

Perpendicular, meaning they have the same slope, hence the given line has a slope of 3/5 based on slope-intercept equation,

y = mx + b

m = 3/5

Determine the slope-intercept form of the given points.

Solution:

In order to determine the slope-intercept form of the given points, we must fist equate the line in point-slope form.

Point-slope form:

y - y1 = m ( x - x1)

Substitute the given values of y1, x1, and m

y - 4 = 3/5 (x - (-9))

y - 4 = 3/5 (x + 9)

Now in order to change into slope-intercept form, we simply needed to distribute 3/5 to each value inside the parenthesis and then transpose -4 on the other side of the equation. We must take note that in transposing a number, the sign changes.

y - 4 = 3/5x + 27/5

y = 3/5x + 27/5 + 4

4 can be written as 20/5

y = 3/5x + 27/5 + 20/5

Slope-Intercept form:

y = 3/5x + 47/5

Final answer:

Slope-Intercept form:

y = 3/5x + 47/5