Question

What is an equation of the line that passes through the point (− 2, 5) and is parallel to the line 3x + 4y = 12 ?

Answer 1

Answer: $y=-\frac{3}{4} x+3.5$ or $y=-\frac{3}{4}x+\frac{7}{2}$

Step-by-step explanation:

A parallel line has the same slope and different y-intercepts.

Let's change our equation to slope-intercept.

$3x+4y=12$

$4y=12-3x$

$y=\frac{12-3x}{4} =3-\frac{3}{4}x$

$y=3-\frac{3}{4} x$

Now that we know our slope is -3/4, we know the equation will have -3/4 as the slope. Let's leave b blank so that we can find the y-intercept of the parallel line.

$5=-\frac{3}{4}(-2)+b$

$5=\frac{3}{2} +b$

$3.5=b$

Our parallel equation is $y=-\frac{3}{4}x+3.5$ or $y=-\frac{3}{4} x+\frac{7}{2}$