Question

50 PTS ANSWER ASAP

What is an equation of the line that passes through the point (−3,2) and is parallel to the line 4x−3y=12?

Answer 1

y = 4/3 x + 6

Explanation:

The first step is to solve for y in the given equation.

4x - 3y = 12 Add 3y to both sides.

4x -3y+3y= 12 + 3y Combine

4x = 12 + 3y Subtract 12 from both sides.

4x-12 = 3y Switch

3y = 4x - 12 Divide by 3

3y/3=4x/3 - 12/3 Do the division

y = (4/3)x - 4

You went to all that trouble so that you could get the slope of the line. The slope is 4/3. It is the number in front of the x that is the slope when the number in front of the y = 1.

Now we need to use the point to get the value of the y intercept in the new line.

x = - 3

y = 2

y = (4/3)x + b where b is the intercept. Substitute

2 = 4/3 * - 3 + b Simplify

2 = - 4 + b Add 4 to both sides.

2 + 4 = b

b = 6

The lines equation is

y = 4/3 x + 6

Answer 2

y-2 = 4/3(x+3) (point slope form)

y = 4/3x+6 slope intercept form

Explanation:

We need to find the slope of the line 4x -3y =12

Solve for y

Subtract 4x from each side

4x-4x -3y = -4x +12

-3y = -4x+12

Divide by -3

-3y/-3 =-4x/-3 +12/-3

y = 4/3 x -4

The slope is 4/3

We want a line that is parallel, so it will have the same slope

We have the slope and a point, so we can use point slope form

y-y1 = m(x-x1)

y-2 = 4/3(x--3)

y-2 = 4/3(x+3)

Distribute

y-2 = 4/3x +4

Add 2 to each side

y-2+2 = 4/3x +4

y = 4/3x +4+2

y = 4/3x+6