Question

write the slope intercept form of the equation of the line describes

through: (-1,-4) parallel to y=6x-2

Answer 1

To find the equation of a line that is parallel to the given line \( y = 6x - 2 \) and passes through the point \((-1, -4)\), we first need to identify the slope of the given line.

The slope of the line \( y = 6x - 2 \) is 6 (since it is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope). Since parallel lines have the same slope, the slope of the new line will also be 6.

Next, we will 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 the point the line passes through and \( m \) is the slope. Substituting in the slope (6) and the point \((-1, -4)\):

\[
y - (-4) = 6(x - (-1))
\]

This simplifies to:

\[
y + 4 = 6(x + 1)
\]

Next, distribute the 6 on the right side:

\[
y + 4 = 6x + 6
\]

Now, isolate \( y \) by subtracting 4 from both sides:

\[
y = 6x + 6 - 4
\]

\[
y = 6x + 2
\]

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

\[
y = 6x + 2
\]