Question

What is the equation in slope-intercept form of the line that passes through the point (6, 3) and is parallel to the graph of y=−23x+12
?

Answer 1

To find the equation of a line that is parallel to another line, we first need to determine the slope of the given line. The equation of the given line is in slope-intercept form, which is \( y = mx + b \), where \( m \) represents the slope.

The equation given is:

\[
y = -23x + 12
\]

From this equation, we can see that the slope \( m \) is \(-23\).

Since parallel lines have the same slope, the slope of the line we are looking for will also be \(-23\).

Now, we 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. We will use the point \( (6, 3) \) and the slope \( -23 \):

\[
y - 3 = -23(x - 6)
\]

Now, we can simplify this equation:

1. Distribute \(-23\):

\[
y - 3 = -23x + 138
\]

2. Add \(3\) to both sides:

\[
y = -23x + 138 + 3
\]

\[
y = -23x + 141
\]

Thus, the equation of the line in slope-intercept form that passes through the point \( (6, 3) \) and is parallel to the line \( y = -23x + 12 \) is:

\[
\boxed{y = -23x + 141}
\]