First let’s review 5.1 y = mx + b

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Presentation transcript:

First let’s review 5.1 y = mx + b Write the equation in slope-intercept form, given m = 3 ang b = (0,-2) Example m = 3, b = (0,-2) y = mx + b y = __ x + ___

Write the equation of the line in slope-intercept form. b = (0,1) y = mx + b

Given this equation, what is the slope and y-intercept? +2x +2x 3y = 2x + 15 3 3 3 m = 2/3 b = (0,5)

Review 5.2 Point-Slope Form

Write the equation of the line in point-slope form. (0,3) Or you can use any point (3,2)

Given (2,3) and slope = -2, write the equation in SLOPE-INTERCEPT This is the equation of the line in point-slope form!! Now leave your answer in slope- intercept form. +3 +3

Given (-8,4) and slope = -3/2, write the equation in SLOPE-INTERCEPT This is the equation of the line in point-slope form!! Now leave your answer in slope- intercept form. +4 +4

5.3 Writing equations of a line given two points

Forms of a linear equation Slope-intercept Form y = mx + b Point-Slope Form y – y1 = m(x – x1)

If given two points, First, find the slope using the slope formula. (x1 , y1) and (x2 , y2) First, find the slope using the slope formula. Example contains (5, –8) and (2, 7) m = 15 –3 m = –5 m = 7 – -8 2 – 5

If given two points, Then use the slope and EITHER point to work like the previous example. y – y1 = m(x – x1) y – 7 = – 5(x – 2) y – 7 = –5x + 10 m = –5, contains (5, –8) and (2, 7) y = –5x + 17

Writing an Equation Given Two Points 1. Calculate the slope of the line. 2. Select the form of the equation. a. Slope-intercept form b. Point-slope form 3. Substitute and/or solve for the selected form.

Writing an Equation Given Two Points Given the two ordered pairs, write the equation of the line in point-slope form. Calculate the slope. or

Writing an Equation Given Two Points in point-slope form:

Same example: Writing an Equation Given Two Points in slope-intercept form. Start by using point-slope form:

2.) Writing an Equation Given Two Points in slope-intercept form. (-5,7) (2,-7) Start by using point-slope form: + 7 + 7 - 7 - 7

EVERY ONE GET A COMMUNICATOR: WITH A BLANK SIDE!!

3.) Writing an Equation Given Two Points in slope-intercept form. (2,0) (-2,6) Start by using point-slope form: + 3 + 3

4.) Writing an Equation Given Two Points in slope-intercept form. (10,-5) (8,4) Start by using point-slope form: - 5 - 5 - 7 - 7

5.) Writing an Equation Given Two Points in slope-intercept form. (6,5) (-3,5) Start by using point-slope form: + 5 + 5 + 5 + 5 Horizontal line

6.) Writing an Equation Given Two Points in slope-intercept form. (-2,-4) (-4,8) Start by using point-slope form: + 7 + 7 - 7 - 7

7.) Writing an Equation Given Two Points in slope-intercept form. (-6,6) (9,1) Start by using point-slope form: + 7 + 7 - 7 - 7

NOW WHAT IF I GAVE YOU A GRAPH, TELL ME THE EQUATION OF THE LINE: WHAT’S THE MAJOR DIFFERENCE BETWEEN THESE TWO GRAPHS: So creating an equation using slope-intercept form would NOT work!!! The one on the right does not have a CLEAN y-intercept!!

Create the equation of the line using two points on the line: (-3,4) (5,8)