Question

35 POINTSThe line contains the point (-8,7) and is perpendicular to 3x+2y=-7 The equation of the line is:

Answer 1

The answer is

`y = (2)/(3) x + (37)/(3)`

Explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the perpendicular line we must first find the slope of the original line

We must first write the equation in the general form above in order to find the slope

3x + 2y = - 7

2y = - 3x - 7

Divide both sides by 2

y = - 3/2x - 7/2

Comparing with the general equation above

Slope = - 3/2

Since the lines are perpendicular to each other the slope of the perpendicular line is the negative inverse of the original line

Slope of perpendicular line = 2/3

So the equation of the line using point (-8,7) and slope 2/3 is

`y - 7 = (2)/(3) (x + 8) \\ y - 7 = (2)/(3) x + (16)/(3) \\ y = (2)/(3) x + (16)/(3) + 7`

We have the final answer as

`y = (2)/(3) x + (37)/(3)`

Hope this helps you