What is an equation of the line that passes through the point (-4,4) and is parallel to the line 3x+2y=14?

Answer 1

Two lines that are parallel have the same slope. In the slope-intercept form of line an equation looks like y=mx+b, where m is the slope, b is the y-intercept and x and y are the coordinates of any point on that line. So, the first thing we need to do is put our given equation into the y=mx+b form:

3x+2y=14 original equation

2y=-3x+14 subtract 3x from both sides to isolate the y term

y=(-3/2)x+14/2 divide both sides by 2 to isolate y

y=(-3/2)x+7 simplify

Now we know that the slope, m, of this equation is -3/2 which will be the same for our new equation because they are parallel. The point-slope form of a line is (y-y₁)=(x-x₁)m, where m is the slope, -3/2, and x₁ and y₁ are the coordinates of any point on that line. In our case we have a point with coordinates (-4,4), so x₁=-4 and y₁=4. Put this information into our formula and we get:

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

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

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

y-4=(-3/2)x-6

y=(-3/2)x-6+4

y=(-3/2)x-2

This is correct, however, most times we want to have the equation in the same form as the other one, that is Ax+By=C, where A, B and C are not fractions. First, multiply everything by 2 to eliminate the slope as a fraction:

y=(-3/2)x-2 our equation

2y=-3x-4 multiply everything by 2 to get rid of the fraction

3x+2y=-4 add 3x to both sides to get our answer

Our new line has the equation 3x+2y=-4.

Answer 2

This equation is written in Standard Format (Ax+By=C). You may, once and forever, convert that to the slope-intercept form of a line and determine that the slope, m = (-A/B).

The slope (m) of parallel lines is the same.

The equation of the parallel line looks like 3x+2y=C and we need the point (-4,4) to determine C.

3(-4) + 2(4) = C

-4 = C

The equation of the parallel line is: 3x + 2y = -4