Question

Write an equation for the line that is parallel to the given line and that passes through the given point.

y = –6x + 2; (–1, 2)


y = –8x – 8


y = 6x – 8


y = –6x – 4


y = –6x + 4

Answer 1

To find the equation of a line that is parallel to the given line \( y = -6x + 2 \) and passes through the point \( (-1, 2) \), we first note that parallel lines have the same slope. The slope of the given line is \(-6\).

Using the slope-intercept form of a line \( y = mx + b \), where \( m \) is the slope, we can write the equation of the parallel line as \( y = -6x + b \).

Next, we need to find the value of \( b \) by substituting the point \( (-1, 2) \) into the equation:

\[
2 = -6(-1) + b
\]

Calculating the right side:

\[
2 = 6 + b
\]

Now, solve for \( b \):

\[
b = 2 - 6
\]
\[
b = -4
\]

Thus, the equation of the line that is parallel to the given line and passes through the point \( (-1, 2) \) is:

\[
y = -6x - 4
\]

Looking at the options provided, the correct answer is:

**y = –6x – 4**