which equations represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4, -2)…

Explanation:

Step1: Find the slope of the given line

Rewrite $3x - 4y=7$ in slope - intercept form $y = mx + b$ (where $m$ is the slope). $-4y=-3x + 7$, so $y=\frac{3}{4}x-\frac{7}{4}$. The slope $m=\frac{3}{4}$. Parallel lines have the same slope.

Step2: Check each option

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

The slope is $-\frac{3}{4}\neq\frac{3}{4}$, so this is not the line.

Option 2: $3x - 4y=-4$

Rewrite in slope - intercept form: $-4y=-3x - 4$, then $y=\frac{3}{4}x + 1$. The slope is $\frac{3}{4}$. Substitute $x=-4$ and $y = - 2$ into the equation: $3\times(-4)-4\times(-2)=-12 + 8=-4$. This line passes through $(-4,-2)$.

Option 3: $4x - 3y=-3$

Rewrite in slope - intercept form: $-3y=-4x - 3$, then $y=\frac{4}{3}x + 1$. The slope is $\frac{4}{3}\neq\frac{3}{4}$, so this is not the line.

Option 4: $y - 2=-\frac{3}{4}(x - 4)$

Rewrite in slope - intercept form: $y-2=-\frac{3}{4}x+3$, then $y=-\frac{3}{4}x + 5$. The slope is $-\frac{3}{4}\neq\frac{3}{4}$, so this is not the line.

Option 5: $y + 2=\frac{3}{4}(x + 4)$

Rewrite in slope - intercept form: $y+2=\frac{3}{4}x+3$, then $y=\frac{3}{4}x + 1$. The slope is $\frac{3}{4}$. Substitute $x=-4$ and $y=-2$ into the equation: $-2 + 2=\frac{3}{4}(-4 + 4)$, which is true. This line passes through $(-4,-2)$.

Answer:

B. $3x - 4y=-4$ E. $y + 2=\frac{3}{4}(x + 4)$