Which equations represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4, -2)? Check all that apply.

Question

I just want to know the answer

Answer 1

Here's another method if you dislike the point-slope form, which many of us do.

 

3x-4y = 7 is your line

We need its slope.  Congruent slopes are PARALLEL.  [Negative reciprocal slopes are PERPENDICULAR.]

 

(1) Convert to y=mx+b (slope intercept form) to find its slope.

3x-4y = 7

-4y = 7-3x [move over the 3x]

y = -(7/4) + (3/4)x [divide both sides by -4]

y = (3/4)x - (7/4) [rearrange]

WHAT IS THIS?  IT IS A LINE WITH A SLOPE OF 3/4 AKA 0.75 AND A Y-INTERCEPT OF -(7/4)

 

(2) Your given line has a slope of 3/4 aka 0.75.  Your PARALLEL line will ALSO have a slope of 3/4 aka 0.75

 

(3) Plug your point (x,y) which was (-4,-2) and your known slope (3/4) into y=mx+b to solve for b (y-intercept)

y = mx+b

-2 = (3/4)(-4) + b [Substitute]

-2 = -3 + b [multiply]

b = 1 [Add 3 to right and left sides to isolate b]

 

(4) REWRITE LINE WITH SLOPE (m) AND Y-INTERCEPT (b)

m = 3/4

b = 1

y = mx + b

y = (3/4)x + 1

y = 0.75x + 1 is also an acceptable answer

 

 

 

 

Answer 2

It will have the equation 3x - 4y = C. We must choose C such that the (-4,-2) satisfies the equation.

 

C = 3x - 4y = 3(-4) - 4(-2) = -12 + 8 = -4

 

The equation is

 

3x - 4y = -4 ← Standard form.

 

y = (3/4)x + 1  ← Slope-Intercept form.

 

y = -2 + (3/4)(x + 4) ← Point-Slope form.