Write the slope-intercept equation for the line that is perpendicular to the line −5x+2y=16 and passes through the point (5,7)

Aleah Avery

Aleah Avery

Answered question

2022-11-13

Write the slope-intercept equation for the line that is perpendicular to the line −5x+2y=16 and passes through the point (5,7)

Answer & Explanation

Cseszteq5j

Cseszteq5j

Beginner2022-11-14Added 17 answers

Given: −5x+2y=16
Add 5x to both sides:
2y=5x+16
Divide both sides by 2:
y = 5 2 x + 8
We can observe that the slope of the line 5 2 . The slope of a line that is perpendicular is the negative reciprocal, - 2 5
The slope-intercept form is:
y = - 2 5 x + b
To find the value of b, substitute in the point (5,7):
7 = - 2 5 ( 5 ) + b
b=9
The equation is:
y = - 2 5 x + 9

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