# Linear and Absolute Value Functions Linear Functions Are

- Slides: 30

Linear and Absolute Value Functions

Linear Functions •

Are these equations linear?

Finding Slope • To find slope (rate of change): – From 2 points—use point-slope formula – From a graph—use rise/run – From an equation—put in slope intercept form – Slope formula:

Find the slope given the following 2 points

Find the slope from the graph

Do these ordered pairs represent linear functions? •

Can a linear equation be used to solve the following problems? 1. A phone company charges $0. 85 for 5 minutes and $1. 10 for 10 minutes. How much will a 20 minute phone call cost? 2. If a projectile is traveling at an initial velocity of 96 ft/sec, how many seconds after launch is the projectile 128 feet above the ground. 3. The hypotenuse of a right triangle is 4 in long. One leg is 1 in longer than the other. Find the lengths of the legs.

Writing Equations of Lines • To write the equation of a line, you must know a point and the slope • Use the point slope formula to write the equation • Put the final equation in slope intercept form

Write the equation of the line • From a point and the slope

Write the equation of the line • From 2 points—must find the slope first

Parallel lines • Parallel lines have the same slope • To write the equation of a line given the parallel line, use the same slope

Parallel lines • To write the equation of a line given the parallel line, use the same slope

Perpendicular lines • Perpendicular lines have opposite reciprocal slopes • To write the equation of a line given the perpendicular line, flip the slope and change the sign

Perpendicular lines • To write the equation of a line given the perpendicular line, flip the slope and change the sign

Perpendicular lines • To write the equation of a line given the perpendicular line, flip the slope and change the sign

Absolute Value Functions • Functions that contain absolute value expressions • Must do two cases to solve—once the abs value is by itself • Absolute value can never equal a negative number because it represents the distance from zero on a number line • Check solutions!!

Solve

Solve

Solve

Graph and Solve

Graph and Solve •

Graph and Solve •

Graph and Solve

Absolute Value Inequalities • Inequalities containing an absolute value expression • Solve just like an absolute value equation • Just remember < “and” > “or” • Special cases when < or > a negative #

Solve and graph. Describe the solution set. •

Solve and graph. Describe the solution set.

Solve and graph. Describe the solution set.

Solve and graph. Describe the solution set.

Solve and graph. Describe solution sets.