2 4 More Linear Equations Point Slope Form

2 -4 More Linear Equations Point Slope Form 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:

Parallel & Perpendicular Lines Write a parallel 32 and p. 86: 10 -21, perpendicular line 35, through the point (6, 2) 60 -62 in slope intercept form Parallel Lines: Slopes are equal Perpendicular Lines: Slopes are negative reciprocal

More Linear Equations Standard Form 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.

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