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2 -3 Linear Functions: Slope Intercept Form Day 1 Objective: I can write and graph a linear function in slope intercept form

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

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

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

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

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

Writing in slope intercept form Solve for y! 18, , 5 1 , 3 1 , 1 1 , p. 78: 9 , 4 4 , 5 3 , 3 3 , 9 19, 23, 27, 2 47 -49

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

Homework Q&A

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

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

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. ? e n i e. L m a S Equation for the line that passes through (7, 3) and (3, 11) OR OR

Graphing from point-slope form Graph the equation: Point: Slope: p. 86: 10 -21, 4244, 49 Exit Ticket Today!!! Slope:

Warm Up Given the pattern above, make an input output table and write an equation in slope intercept form for the diagram number and the squares per diagram:

Homework Q&A

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

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

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

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

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: (y-intercept) Slope-intercept Form

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. p. 86: 22 -31, 36 -41 If both trucks are used for different amounts of time to pump out the basement, write an equation to represent this situation. Time spent pumping x = First Truck y = Second Truck Amount of + = Total water 1 st Truck water 2 nd Truck Standard Form