### Linear Functions and Slope

**linear function**is a function whose graph is a line. All linear functions can be written in the form:

**slope**is the ratio of the change in $y$ to the change in $x$ for two points on a line, represented as:

- The
**rise**is the vertical change between two points on a line. - The
**run**is the horizontal change between two points on a line.

**is the value of $y$ where a graph touches or crosses the $y$-axis. Linear functions can also be written in slope-intercept form using $y$ in place of $f(x)$:**

*y*-interceptDetermine the slope and intercept of the line.

The slope is the coefficient of $x$, or $m=2$.

The $y$-intercept is the constant term, which is also the value of $f(0)$, or $b=3$.Identify the slope.

The slope is the coefficient of the $x$-term.Identify the $y$-intercept.

The $y$-intercept is the constant term.### Rate of Change of a Linear Function

Suppose two cars are traveling at constant speeds. Car 1 travels at 90 kilometers per hour (km/h), while Car 2 travels at 100 km/h.

Graph the distance traveled over time for the two cars. Then compare the rates of change.

- Car 1: $f(x)=90x$
- Car 2: $f(x)=100x$

Determine two points on each linear function by using the slope and $y$ -intercept.

For Car 1:

The $y$ -intercept is zero. So, one of the points is $(0, 0)$.

From $(0, 0)$, use the slope of 90 to find another point. The rise is 90, and the run is 1. So, the second point is at $(1, 90)$.

For Car 2:

The $y$-intercept is zero. So, one of the points is $(0, 0)$.

From $(0, 0)$, use the slope of 100 to find another point. The rise is 100, and the run is 1. So the other point is $(1, 100)$.