Question

select the correct answer.
which equation represents the line that is parallel to $y = \frac{3}{7}x + 11$ and passes through (-21,42)?
\bigcirc a. $y = -\frac{7}{3}x - 7$
\bigcirc b. $y = -\frac{7}{3}x + 77$
\bigcirc c. $y = \frac{3}{7}x - 39$
\bigcirc d. $y = \frac{3}{7}x + 51$

Explanation:

Step1: Determine the slope of the parallel line

Parallel lines have the same slope. The given line is \( y = \frac{3}{7}x + 11 \), so the slope \( m \) of the line we want is \( \frac{3}{7} \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(-21,42) \) and \( m = \frac{3}{7} \).
Substitute the values into the formula:
\( y - 42=\frac{3}{7}(x+ 21) \)

Step3: Simplify the equation

First, distribute \( \frac{3}{7} \) on the right - hand side:
\( y - 42=\frac{3}{7}x+\frac{3\times21}{7} \)
Since \( \frac{3\times21}{7}=3\times3 = 9 \), the equation becomes:
\( y - 42=\frac{3}{7}x + 9 \)
Then, add 42 to both sides of the equation:
\( y=\frac{3}{7}x+9 + 42 \)
\( y=\frac{3}{7}x+51 \)

Answer:

D. \( y=\frac{3}{7}x + 51 \)