Question

Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options.

Answer 1

Answer:

$y= \frac{3}{4} x +1$

Step-by-step explanation:

To know wich equation represent the line that is parallel to 3x-4y=7, first we are going to isolate y:

$-4 y= 7 - 3x\\y= \frac{7-3x}{-4}\\y= \frac{-7}{4} + \frac{3}{4}x$

So the slope of this function is $\frac{3}{4}$. The lines are parallel, so this means that both functions have the same slope.

So far we know that:

$y= \frac{3}{4} x +b$

In order to know b's value, we have to supplant the point (-4:-2) on our equation:

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

$-2= -3 +b$

$-2+3=b$

$1=b$

So the equation that represents the line that is parallel to the given function, has the following equation:

$y= \frac{3}{4} x +1$