Question

What is an equation of the line that passes through the point (3,-3) and is perpendicular to the line 3x+2y=12 ?

Answer 1

Answer:

y=2/3x-5

Step-by-step explanation:

1. find the slope of the given line

2. find its opposite reciprocal(slope of the perpendicular line)

3. create a new linear equation using the new slope

4. substitute (3,-3) to find b

Answer 2

Answer:y = 2x/3 - 5

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

3x+2y=12

We would rearrange it so that it will form of the y = mx + c. It becomes

2y = -3x + 12

y = -3x/2 + 6

Comparing with the slope intercept form, slope = - 3/2

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the given line. Therefore, the slope of the line passing through (3,-3) is 2/3

To determine the intercept, we would substitute m = 2/3, x = 3 and y = -3 into y = mx + c. It becomes

- 3 = 2/3×3 + c = 2 + c

c = - 3 - 2 = - 5

The equation becomes

y = 2x/3 - 5