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ahrayia [7]
3 years ago
15

Create the equation of a line that perpendicular to 2y=14+2/3x and passes through the point (-2,8).

Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
4 0

Answer:

y = - 3x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2y = 14 + \frac{2}{3} x into this form

Divide all terms by 2

y = 7 + \frac{1}{3} x ← in slope- intercept form

with slope m = \frac{1}{3}

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{\frac{1}{3} } = - 3, hence

y = - 3x + c ← is the partial equation of the perpendicular line

To find c substitute (- 2, 8) into the partial equation

8 = 6 + c ⇒ c = 8 - 6 = 2

y = - 3x + 2 ← equation of perpendicular line

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