Question

The function f(x) is shown in the graph. What is the equation for f(x)?

Answer 1

It's a linear graph, so we can use the slope-intercept form. Let's find the y-intercept first, which happens ar y = -3. Now let's find the slope. To do so, let's pick two points on the graph (relatively easy ones): (0, -3) and (5, -7). 

Let's find the slope:
$m = \frac{y_2-y_1}{x_2-x_1} = \frac{-7-(-3)}{5-0} = -\frac{4}{5}$

Let's write it in slope-intercept form. Recall that slope-intercept form is:
$y = mx+b$

Where m = slope and b = y-intercept. We have all the parts, so let's write it:
$y = -\frac{4}{5}x - 3$