write an equation in slope-intercept form of the line passing through (-9,5) and is perpendicular to the line y= -3x+2

Answer 1

The slope-intercept form of the equation of a line is y=mx + b

where m=slope

b = y-intercept

The slope, m, of this line is -3.

The slope of all parallel lines is (+1/3). [the negative reciprocal]

That means the the parallel line has an equation that looks like: y = (1/3)x + b

This line passes through (-9,5), so:

5 = (1/3)(-9) + b

5 = -3 + b

8 = b

The equation of the parallel line is: y = (1/3)x + 8

Answer 2

The line y = -3x + 2 has a slope of -3 or -3/1

The perpendicular slope would be the "flip and negate" or +1/3

Use this in y=mx+b with your point (-9,5) as your x and y

5 = (+1/3)(-9) + b to find the y-intercept "b"

5 = -3 + b

b = 8

So the equation of the perpendicular line is:

y = (1/3)x + 8