Writing Linear Equations in Slope-Intercept Form

To write the equation of a line in the slope-intercept form, we must first find both the slope $m$ and the $y$-intercept $b.$ The line's $b$-value is the $y$-coordinate of the point where the line crosses the $y$-axis.

We see that the $b$-value is $0.5$. To determine the line's slope, we measure the difference in the $y$-direction between two points on the graph that are $1$ step away from each other in the $x$-direction.

The difference in the $y$-direction is $\text{-} 0.5$ because the line decreases by 0.5 when moving one step to the right in the $x$-direction. The line's slope is $m = \text{-} 0.5$ and by substituting the $m$ and $b$-values into the equation of a line, we get $y=\text{-} 0.5 x+0.5.$