Warm Up What are the slopes and y-intercepts in the following equations : y = 11x +4 3y + 2 = 6x Find the slope given points: (6,7) and (15,2). m = 11 y = 4 y = m = 2

Linear Functions: Slope Intercept Form Objective: I can write and graph a linear function in slope intercept form 2-3

Slope Vertical Change Horizontal Change Vertical Change (rise) Horizontal Change (run) (x 2, y 2 ) (x 1, y 1 ) Sketch and describe the slopes of each graph. Positive Slope Negative Slope Slope = 0 undefined

Find the slope for each set of points. (1,7) and (6, 4) (-4, -5) and (5, 6) (x 1, y 1 ) and (x 2, y 2 ):

Slope = m y-intercept = b Linear Equation: Slope Intercept form m = 2; y-intercept is (0, -3) m = ; y-intercept is (0, 7) 7

Linear Equation: Slope Intercept form Vertical Change Horizontal Change Vertical Change Horizontal Change

Linear Equation: Slope Intercept form Graph: 1. Plot y-intercept 2. Use slope to plot 2 nd point. 3. Draw line through points. Vertical Change Horizontal Change Graph:

Writing in slope intercept form Solve for y! p.78: 9, 11, 13, 15, 18, 19, 23, 27, 29, 33, 35, 44, 47-49

Five pop machines have been reported malfunctioning. In an effort to diagnose the problem, 30 trials have been recorded. The left column indicates the button pushed, the right column indicates the can received. Which of the machines are truly malfunctioning?

Warm Up What are the x and y intercepts? 3x + y = 6 Calculate the slope given points (2,3) and (4,5)

2-3 More Linear Equations Point Slope Form Objective: I can write and graph a linear function in point slope form. Day 2

Point Slope Form Slope Formula: Point (2, 3) Slope: 4 Examples Point (-3, -7) Slope: Point (-6, 5) Slope: Slope Point (x 1, y 1 )

Write an equation given two points Equation for the line that passes through (3, 2) and (5, 8) 1. Find the slope. 2. Choose 1 of the given points and substitute into point-slope form. OR Same Line? Equation for the line that passes through (7, 3) and (3, 11) OR

Graphing from point-slope form Graph the equation: Point:Slope: Graph the equation: Point:Slope: p. 86:11-21 odd, (use graph paper)

Warm Up Write an example of an equation in: Y-intercept form Point Slope form

More Linear Equations Standard Form Objective: I can write and graph a linear function in standard form. Day 3

Standard Form: Point Slope Form: Slope-Intercept Form: Three Forms of a linear equation y = mx + b y – y 1 = m(x – x 1 ) Ax + By = C where A, B, and C are integers. - meaning no fractions or decimals. m = slopeb = y-intercept m = slope(x 1, y 1 ) = point

Solve for y! Standard Form to Slope-Intercept Form No fractions or decimals Slope-Intercept Form to Standard Form Add or Subtract mx from both sides. Multiply to eliminate denominators. Ax + By = C

Graphing a standard form equation Find and graph the intercepts. x-intercept y-intercept 3x + 5y = 15 x = ___________ y = _________ x = y =

A runner is participating in a 10-kilometer road race and she is currently at the halfway point. She looks at her watch and notices that it has taken her exactly twenty five minutes to get to this point. Assume that she has run at a constant rate and will complete the race at this same rate. Write an equation to represent the distance she has run from where she is now. x = Time (minutes) y = Distance from 5 km (km) Running Rate: Starting point: Slope-intercept Form (y-intercept)

After a water main break, a large building’s basement was flooded to the ceiling. The local fire department provides two pump trucks to pump the water out. The first truck can pump 25 cubic feet of water per minute and the second truck can pump 32 cubic feet of water per minute. The building is a rectangular prism, measuring 150 feet long, 120 feet wide and 10 feet deep. Time spent pumping x = First Truck y = Second Truck If both trucks are used for different amounts of time to pump out the basement, write an equation to represent this situation. Standard Form Amount of water 1 st Truck + Amount of water 2 nd Truck = Total p.86:10-21, , 60-62