Question

Write an equation for a line parallel to Y=-2x-1 and passing through the point (4,-6).
y=

Answer 1

To find the equation of a line parallel to the given line \( y = -2x - 1 \) and passing through the point \( (4, -6) \), we need to do the following:

1. Determine the slope of the given line. The equation \( y = -2x - 1 \) is in slope-intercept form \( y = mx + b \), where \( m \) is the slope. Here, the slope \( m \) is \( -2 \).

2. Since parallel lines have the same slope, the slope of the new line will also be \( -2 \).

3. We can use the point-slope form of the equation of a line, which is given by:

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

where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.

4. Plugging in the slope \( -2 \) and the point \( (4, -6) \):

\[
y - (-6) = -2(x - 4)
\]

5. Simplifying this equation:

\[
y + 6 = -2(x - 4)
\]
\[
y + 6 = -2x + 8
\]
\[
y = -2x + 8 - 6
\]
\[
y = -2x + 2
\]

Thus, the equation of the line parallel to \( y = -2x - 1 \) and passing through the point \( (4, -6) \) is:

\[
y = -2x + 2
\]