Graphing Linear Functions in Slope-Intercept Form

Equations written in slope-intercept form follow a specific format. $y=mx+b$ Here, $m$ represents the slope of the line and $b$ represents the $y\text{-}$intercept. Let's identify the slope and the $y\text{-}$intercept in our equation. $y={\color{#0000FF}{m}}x+{\color{#009600}{b}} \quad \Leftrightarrow \quad y={\color{#0000FF}{\text{-} \dfrac{1}{2}}}x+{\color{#009600}{5}}$ The slope is ${\color{#0000FF}{\text{-} \frac{1}{2}}}$ and the $y$-intercept is ${\color{#009600}{5}}.$

Graphing the Equation

Since the $y$-intercept is $5$ we know that the point $(0,5)$ is on the graph. We can use that the slope, $m,$ is $\text{-} \frac{1}{2}$ to find another point on the graph. $m=\dfrac{{\color{#0000FF}{\Delta y}}}{{\color{#009600}{\Delta x}}} \quad \Rightarrow \quad m=\text{-} \dfrac{1}{2}= \dfrac{{\color{#0000FF}{\text{-} 1}}}{{\color{#009600}{2}}}$ Thus, we can can find another point by first moving $2$ units in the positive horizontal direction and then $1$ unit in the negative vertical direction.

To graph the equation we will now connect the two points with a line.

Identify the $x$-intercept

Now that we have graphed the given function, we can use our graph to identify the $x\text{-}$intercept. This is the point at which the line intercepts the $x\text{-}$axis.

The line crosses the axis at $(10,0),$ so the $x\text{-}$intercept is $10.$