Question

Find the equation of the line through point (−2,−2) and parallel to 3x+4y=12. Use a forward slash (i.e. "/") for fractions (e.g. 1/2.

Answer 1

Answer:

3x + 4y = - 14

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x + 4y = 12 ( subtract 3x from both sides )

4y = - 3x + 12 ( divide all terms by 4 )

y = - $\frac{3}{4}$ x + 3 ← in slope- intercept form

with slope m = - $\frac{3}{4}$

Parallel lines have equal slopes, thus

y = - $\frac{3}{4}$ x + c ← is the partial equation

To find c substitute (- 2, - 2) into the partial equation

- 2 = $\frac{3}{2}$ + c ⇒ c = - $\frac{7}{2}$

y = - $\frac{3}{4}$ x - $\frac{7}{2}$ ← in slope- intercept form

Multiply through by 4 to clear the fractions

4y = - 3x - 14 ( add 3x to both sides )

3x + 4y = - 14 ← in standard form