# Find the equation of the line passing through the point (3,-2) with x-intercept -4.

## Question:

Find the equation of the line passing through the point (3,-2) with {eq}x- {/eq}intercept -4.

## Lines:

When we have two points on a line, we can find the line's slope:

{eq}\begin{align*} m &= \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1} \end{align*} {/eq}

With the slope and a point on the line, we can use the point-slope form of a line to write its equation:

{eq}\begin{align*} y - y_1 &= m(x - x_1) \end{align*} {/eq}

Since the {eq}x {/eq} intercept is where {eq}y = 0 {/eq} (we more commonly call them zeroes), we know the point {eq}(-4,0) {/eq} is on the line. We will use this as our {eq}(x_1, y_1) {/eq}. Then we also have {eq}(x_2, y_2) = (3, -2) {/eq} and so the slope of the line is

{eq}\begin{align*} m &= \frac{y_2 - y_1}{x_2 - x_1} \\ &= \frac{-2-0}{3-(-4)} \\ &= - \frac27 \end{align*} {/eq}

Then the equation of the line passing through the two points is

{eq}\begin{align*} y - 0 &= - \frac27 (x - (-4) ) \\ y &= - \frac27x - \frac87 \end{align*} {/eq}