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

Option A: $y=\frac{3}{4}x+1$ is the equation of the line.

Option E: $y+2=\frac{3}{4}(x+4)$ is the equation of the line.

Explanation:

Given that the line is $3 x-4 y=7$ and passes through the point $(-4,-2)$

We need to determine the equation of the line.

Formula:

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

Slope:

Since, the lines are parallel, from the equation $3 x-4 y=7$, we shall determine the slope.

Thus, we have,

$-4 y=-3x+7$

   $y=\frac{3}{4} x+\frac{7}{4}$

Thus, the slope of the equation is $m=\frac{3}{4}$

Equation of line:

Substituting $m=\frac{3}{4}$ and the point $(-4,-2)$ in the formula, we get,

$y+2=\frac{3}{4}(x+4)$

Hence, the equation of line is $y+2=\frac{3}{4}(x+4)$

Thus, Option E is the correct answer.

Let us write the equation of line $y+2=\frac{3}{4}(x+4)$ in slope - intercept form.

Thus, we have,

$y+2=\frac{3}{4}x+3$

     $y=\frac{3}{4}x+3-2$

     $y=\frac{3}{4}x+1$

Thus, the equation of the line is $y=\frac{3}{4}x+1$

Hence, Option A is the correct answer.