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

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 slope formula:

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

Taking the points \((-3, 4)\) as \((x_1, y_1)\) and \((-6, 3)\) as \((x_2, y_2)\):

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

Now that we have the slope \(m = \frac{1}{3}\), we can use the point-slope form of the line equation, which is:

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

We can use either point, but let's use the point \((-3, 4)\):

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

Now, we can simplify this equation:

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

Next, isolate \(y\) 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:

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