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)

Answer 1

The equation of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) can be found using the slope-intercept form equation \((y - y_1) = m(x - x_1)\), where \(m\) is the slope of the line.

First, we need to find the slope of the line.

Slope (\(m\)) = \(\frac{y_2 - y_1}{x_2 - x_1}\)

Substituting the coordinates of the points (-3,4) and (-6,3) into the slope formula, we get:

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

Now that we have the slope \(m = \frac{1}{3}\), we can use either of the given points to find the y-intercept.

Let's use the first given point (-3, 4) to find the y-intercept (\(b\)).

Substituting the coordinates \((x_1, y_1) = (-3, 4)\) and the slope \(m = \frac{1}{3}\) into the slope-intercept form equation \((y - y_1) = m(x - x_1)\), we get:

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

Expanding the equation:

\(y - 4 = \frac{1}{3}x + 1\)
\(y = \frac{1}{3}x + 1 + 4\)
\(y = \frac{1}{3}x + 5\)

So, the equation of the line that passes through the points (-3,4) and (-6,3) in slope-intercept form is \(y = \frac{1}{3}x + 5\).