Question

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 first need to determine the slope (m) of the line using the formula:

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

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

Substituting the values, we get:

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

Now that we have the slope, we can use the point-slope form of the equation. The point-slope form is given by:

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

Using point \((-3, 4)\):

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

Now, distribute \(\frac{1}{3}\):

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

Next, solve for \(y\) by adding 4 to both sides:

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

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

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