Question

What is the equation of the line that passes through the points (−3,4)
and (−6,3)
? Write the answer in slope-intercept form.(1 point)
y=
(
)x+

Answer 1

To find the equation of the line that passes through the points \((-3, 4)\) and \((-6, 3)\), we need to determine the slope and then use the point-slope form of a line.

1. **Calculate the slope (m)**:

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Plugging in our points:

- \((x_1, y_1) = (-3, 4)\)
- \((x_2, y_2) = (-6, 3)\)

\[
m = \frac{3 - 4}{-6 - (-3)} = \frac{-1}{-6 + 3} = \frac{-1}{-3} = \frac{1}{3}
\]

2. **Use the point-slope form to find the equation**:

The point-slope form of the equation of a line is given by:

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

Using the slope \(m = \frac{1}{3}\) and the point \((-3, 4)\):

\[
y - 4 = \frac{1}{3}(x + 3)
\]

3. **Convert to slope-intercept form (y = mx + b)**:

First, distribute on the right side:

\[
y - 4 = \frac{1}{3}x + 1
\]

Now, add 4 to both sides:

\[
y = \frac{1}{3}x + 1 + 4
\]
\[
y = \frac{1}{3}x + 5
\]

So, the equation of the line in slope-intercept form is:

\[
\boxed{y = \frac{1}{3}x + 5}
\]