# Graphing Linear Functions in Slope-Intercept Form

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## Slope-Intercept Form

One way to express linear function rules is called slope-intercept form.

$y=mx+b$

Sometimes, $f(x)=mx+b$ is used. In either case, $m$ and $b$ describe the general characteristics of the line. $m$ indicates the slope, and $b$ indicates the $y$-intercept. The linear function graphed below can be expressed as $f(x)=2x+1,$ because it has a slope of $2$ and a $y$-intercept at $(0,1).$

## Graphing a Linear Function in Slope-Intercept Form

To graph a line in slope-intercept form, the slope, $m,$ and the $y$-intercept, $b,$ are both needed. Consider the linear function $y=2x-3.$ Since the rule is written as $y=mx+b,$ it can be seen that $m=2 = \dfrac{2}{1} \quad \text{and} \quad b=\text{-} 3.$ To graph the line, plot the $y$-intercept, then use the slope to find another point on the line. Specifically, from $(0,\text{-} 3),$ move up $2$ units and right $1$ unit.

Next, draw a line through both points to create the graph of the linear function.

## Describing Key Features of Linear Functions

## Solving Linear Equations Graphically

The function $y=f(x)$ is comprised of all the $(x,y)$ points that satisfy its function rule. For example, some of the points that lie on the line $y=x+3$ are $(\text{-} 1,2), \quad (0,3), \quad (1,4), \quad (2,5).$

All of the $x$-$y$ pairs that satisfy an equation are the points on the corresponding graph. Thus, the solution(s) to an equation can be found using a graph.## Exercises

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