Answer
$y = -\frac{4}{5}x + \frac{16}{5}$
Work Step by Step
Because we are given a point on the graph along with the slope, it makes sense for us to use the point-slope form of an equation, which is given by the following formula:
$y - y_1 = m(x - x_1)$
where $m$ is the slope of the graph and $(x_1, y_1)$ is a point on that graph.
Substitute $m=-\frac{4}{5}, x=-1. \quad \text{and} \quad y=4$ into the point-slope form above to obtain:
$y - 4 = -\frac{4}{5}[x - (-1)]$
$y - 4 = -\frac{4}{5}(x + 1)$
Distribute the right side to simplify:
$y - 4 = -\frac{4}{5}x - \frac{4}{5}$
Convert this equation into the slope-intercept form by adding $4$ to each side of the equation and isolating $y$ on the left side of the equation:
$y = -\frac{4}{5}x - \frac{4}{5} + 4$
$y = -\frac{4}{5}x - \frac{4}{5} + \frac{20}{5}$
$y = -\frac{4}{5}x + \frac{16}{5}$
