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# Graphing Linear Functions in Slope-Intercept Form

## Graphing Linear Functions in Slope-Intercept Form 1.7 - Solution

a

The function rule is written in slope-intercept form, $y=mx+b.$ First we want to identify the line's slope, $m,$ and $y$-intercept, $b.$ $y={\color{#0000FF}{3}}x {\color{#009600}{-9}} \quad \quad \quad m={\color{#0000FF}{3}} \text{ and } b={\color{#009600}{\text{-} 9}}$ We can see that the $y$-intercept is $b=\text{-} 9.$ Therefore, the graph crosses the $y$-axis at $(0,\text{-} 9).$ The slope, $m,$ is $3.$ This means that the line increases by $3$ units in the $y$-direction while moving $1$ unit to the right in the $x$-direction. Using this we can find two points on the line.

We can draw the graph of the function by connecting the points with a line.

We can now with words describe what this graph looks like. When moving $1$ unit to the right, the line increases by $3$ units. The line crosses the $y$-axis at $y=\text{-}9.$

b

We need to find the line's slope and $y$-intercept. For a line written in slope-intercept form, $y=mx+b,$ the slope is $m$ and the $y$-intercept is $b.$ $y={\color{#0000FF}{\text{-}2}}x+{\color{#009600}{5}} \quad \quad \quad m={\color{#0000FF}{\text{-}2}} \text{ and } b={\color{#009600}{5}}$ We have a $y$-intercept of $b=5.$ This means that the function crosses the $y$-axis when $y = 5.$ The slope is $\text{-}2,$ which means that the line decreases by $2$ units in the $y$-direction while moving $1$ unit to the right in the $x$-direction. We can use this to find two points on the graph.

Let's draw the graph of the function. We do that by connecting the points with a line.

We are ready to describe what the graph looks like. When moving $1$ unit to the right, the line decreases by $2$ units. The line crosses the $y$-axis at $y=5.$