Question

Write an equation of the line that passes through (−4,3)
and is parallel to the line y=−32x−6

.(1 point)
An equation of a parallel line is

Answer 1

To find the equation of a line that is parallel to the line given by \( y = -32x - 6 \) and passes through the point \( (-4, 3) \), we first identify the slope of the given line.

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope. From the equation \( y = -32x - 6 \), we can see that the slope \( m \) is \( -32 \).

Since parallel lines have the same slope, the slope of the new line will also be \( -32 \).

Now, we use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Here, \( (x_1, y_1) \) is the point the line passes through, and \( m \) is the slope. Substituting \( m = -32 \), \( x_1 = -4 \), and \( y_1 = 3 \):

\[
y - 3 = -32(x + 4)
\]

Next, we simplify the equation:

\[
y - 3 = -32x - 128
\]
\[
y = -32x - 128 + 3
\]
\[
y = -32x - 125
\]

Thus, the equation of the parallel line is:

\[
\boxed{y = -32x - 125}
\]