Chapter 3: Functions and Graphs Section 3.6 & 3.8: The Slope of a Line & Equations of a Line.

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Presentation transcript:

Chapter 3: Functions and Graphs Section 3.6 & 3.8: The Slope of a Line & Equations of a Line

Section 3.6 & 3.8: The Slope of a Line Equations of Lines Goal: To find the slope of a line, to use the slope and y-intercept to write an equation of a line, and to graph a linear equation. Also, to write an equation of a line, given the slope and a point on the line and to write an equation of a line, given two points.

Section 3.6 & 3.8: The Slope of a Line & Equations of Lines Slope – ratio of the change in y-coordinates to the corresponding change in x-coordinates. If a line passes through points (x 1, y 1 ) and (x 2, y 2 ), then: slope = change in y-coordinates = y 2 – y 1 change in x-coordinates x 2 – x 1 slope (m)

Section 3.6 & 3.8: The Slope of a Line & Equations of Lines Example 1 Find the slope of the line that passes through (1, 3) and (-2, -3). Then graph the line.

Section 3.6 & 3.8: The Slope of a Line & Equations of Lines If the line rises to the right, then the slope is positive (-2, -2) and (3, 3) If the line is horizontal, then the slop is zero (-3, 2) and (3, 2) If the line falls to the right, then the slope is negative (0, 3) and (3,0) If the line is vertical, then the slope is undefined (-2, 3) and (-2, -2)

Section 3.6 & 3.8: The Slope of a Line & Equations of Lines Slope – intercept form – The slope-intercept form of the equation of a line is y = mx + b m is the slope b is the y-intercept

Section 3.6 & 3.8: The Slope of a Line & Equations of Lines If you are given the slope and y-intercept of a line, you can find an equation of the line Example: Write an equation of a line that has a slope of -2 and a y-intercept of 5 You can also use slope-intercept form to find an equation of a line if you know slope and the coordinates of any point

Section 3.6 & 3.8: The Slope of a Line & Equations of Lines Point – slope form – The point-slope form of the equation of a line is y – y 1 = m (x – x 1 ) (x 1, y 1 ) are the coordinates of a point on the line m is the slope

Section 3.6 & 3.8: The Slope of a Line & Equations of Lines Example 1 Write an equation in slope-intercept form for the line that has a slope of -3/5 and passes through (5, -2)

Section 3.6 & 3.8: The Slope of a Line & Equations of Lines Example 2 What is an equation of the line though (2, -3) and (-3, 7)?

Section 3.6 & 3.8: The Slope of a Line & Equations of Lines Example 3 As a part-time salesperson, Jean Stock is paid a daily salary plus commission. When her sales are $100, she makes $58. Then her sales are $300, she makes $78. Write a linear equation to model this situation

Section 3.6 & 3.8: The Slope of a Line & Equations of Lines Example 3 (cont.) What are Ms. Stock’s daily salary and commission rate? How much would Jean make in a day if her sales were $500?

Section 3.6 & 3.8: The Slope of a Line & Equations of Lines Homework: Practice Exercises Pg. 121 #2-40 (even) Practice Exercises Pg. 129 #2-8 (even)