Question

The given line passes through the points (0, ) and (2, 3).

On a coordinate plane, a line goes through (0, negative 3) and (2, 3). A point is at (negative 1, negative 1).

What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point ()?

Answer 1

To find the equation of a line that is parallel to another line and passes through a specific point, we first need to determine the slope of the given line.

The given points through which the line passes are (0, -3) and (2, 3). We can calculate the slope (\(m\)) of the line using the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Plugging in the coordinates:

\[
m = \frac{3 - (-3)}{2 - 0} = \frac{3 + 3}{2} = \frac{6}{2} = 3
\]

So, the slope of the given line is \(3\).

Lines that are parallel have the same slope. Therefore, the slope of the line we are trying to find is also \(3\).

Next, we need to find the equation of the line that has this slope and passes through the point (-1, -1). We can use the point-slope form of the equation of a line, which is given by:

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

Using the point (-1, -1) and the slope \(m = 3\):

\[
y - (-1) = 3(x - (-1))
\]

This simplifies to:

\[
y + 1 = 3(x + 1)
\]

So, the equation of the line in point-slope form that is parallel to the given line and passes through the point (-1, -1) is:

\[
y + 1 = 3(x + 1)
\]