I dont know how to work this out.

Question

Write an equation of the line that passes through (-3,3) and is perpendicular to the line 2y=8x-6.

Answer 1

Hello, Lydia,

I just answered a similar question for you, so I'll make this one short. Please refer to the first question and se if it helps you through this one.

Rewrite the equation is standard form: y = 2x - 3

Remember that a perpendicular line has a slope, m, that is the negative inverse. In this case it would become -1/2.

So far, we have y = -(1/2)x + b. Determine b by plugging in the point on the line that was provided (-3,3). By solving for b, you'll have what you need for the perpendicular line passing through (-3,3).

Bob

3 = -(1/2)(-3) + b

3 = 3/2 + b

b = 1.5

Answer 2

Hi Lydia A

y = (-1/4)x + 9/4

Write an equation of the line that passes through (-3,3) and is perpendicular to the line 2y=8x-6.

First you put the line in Slope Intercept form by setting everything equal to y

In the Slope Intercept Form, the coefficient of x is the slope, m

A line perpendicular will have a slope that is the opposite inverse of the x coefficient

Once you get that far you will solve for b, by using the coordinates (-3,3)

2y = 8x - 6

Solved for y is

y = 4x - 3

So the slope, which I mentioned above is the coefficient of x, is 4

A perpendicular with have the opposite inverse of 4, (-1/4) as the slope and in Slope Intercept Form looks like

y = (-1/4)x + b

Now we need to find b, use (-3,3) in the equation above to solve for b

3 = (-1/4)(-3) + b

3 = 3/4 + b

3 - 3/4 = b

12/4 - 3/4 = b

9/4 = b

Your perpendicular line is

y = (-1/4)x + 9/4

You can graph this line and the line you were given to see that they are in fact Perpendicular and that the perpendicular line passes through (-3,3) at Desmos.com