Write an equation in slope-intercept form for the line that passes through (-3, 5), and is perpendicular to the graph of 5x - 6y = 9

y=(-6/5)x+8.6

Step-by-step explanation:

If a line is perpendicular to 5x-6y=9, then it must have a slope that is the negative reciprocal.

1) Fine the slope of the first line by setting the equation equal to y.

5x-6y=9

5x-9= 6y

(5/6)x-1.5=y

slope= 5/6

2) Find the negative reciprocal of the slope

slope: 5/6

reciprocal: 6/5

negative reciprocal: -6/5

3) We now get to use the points (-3, 5) by plugging them into slope-intercept form. The goal is finding the y-intercept.

y=mx+b

5=(-6/5)(-3)+b

5=(-18/5)+b

5= -3.6+b

b= 8.6

4) Now we put everything back in slope-intercept form.

y=(-6/5)x+8.6

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