Graphing Linear Functions in Slope-Intercept Form

Let's recall the slope-intercept form of a line. $$y=mx+b$$ Here, $m$ represents the slope and $b$ the $y\text{-}$intercept. Let's identify the slope and the $y\text{-}$intercept of the line in the graph.

Finding the $y$-intercept

Consider the given graph.

We can see that the function intercepts the $y\text{-}$axis at the point $(0,2).$ This means the $y\text{-}$intercept is $b=2.$

Finding the Slope

To find the slope, we will trace along the line of the given graph until we find a lattice point, which is a point that lies perfectly on the grid lines. By doing this, we will be able to identify the slope using rise and run of the graph.

Here we have identified $(5,\text{-}1)$ as our second point. From the $y\text{-}$intercept to this point, we move $5$ steps horizontally in the positive direction. Then, we move $3$ steps vertically in the negative direction. $$m=\frac{\text{rise}}{\text{run}}=\frac{\text{-}3}{5}\iff m=\text{-}\frac{3}{5}$$

Writing the Equation

Now that we have the slope and the $y\text{-}$intercept, we can write our final equation. $$y=mx+b\Rightarrow y=\text{-}\frac{3}{5}x+2$$ The correct choice is D.