Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 10 Graphing Equations and Inequalities

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Equations of Lines

Martin-Gay, Developmental Mathematics, 2e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. When a linear equation in two variables is written in slope-intercept form, y = mx + b then m is the slope of the line and (0, b) is the y-intercept of the line. Slope-Intercept Form slope (0, b), y-intercept Note: This form is useful for graphing, since you have a point and the slope readily visible.

Martin-Gay, Developmental Mathematics, 2e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Use the slope-intercept form to graph the equation The slope is 3/5. The y-intercept is –2. Begin by graphing (0, –2), move up 3 units and right 5 units.

Martin-Gay, Developmental Mathematics, 2e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. First, we need to solve the linear equation for y. By adding 3x to both sides, y = 3x – 5. Once we have the equation in the form of y = mx + b, we can read the slope and y-intercept. slope is 3 y-intercept is (0, –5) Example Find the slope and y-intercept of the line –3x + y = –5.

Martin-Gay, Developmental Mathematics, 2e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Find an equation of the line with y-intercept (0, –2) and slope of. We are given the slope and the y-intercept. We let m = and b = –2 and write the equation in slope-intercept form, y = mx + b. y = mx + b Example

Martin-Gay, Developmental Mathematics, 2e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. The point-slope form of the equation of a line is where m is the slope of the line and (x 1, y 1 ) is a point on the line. Point-Slope Form,

Martin-Gay, Developmental Mathematics, 2e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Find an equation of the line with slope –2 that passes through (–11, –12). Write the equation in slope-intercept form, y = mx + b, and in standard form, Ax + By = C. We substitute the slope and point into the point-slope form of an equation. y – (–12) = – 2(x – (– 11)) Let m = –2 and (x 1, y 1 ) = (–11, –12). y + 12 = –2x – 22 Use the distributive property. y = –2x – 34 Slope-intercept form. 2x + y = –34 Add 2x to both sides and we have standard form. Example

Martin-Gay, Developmental Mathematics, 2e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Find the equation of the line through (–4, 0) and (6, –1). Write the equation in standard form. First, find the slope. Example continued

Martin-Gay, Developmental Mathematics, 2e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Now substitute the slope and one of the points into the point-slope form of an equation. Clear fractions by multiplying both sides by 10. Use the distributive property. Add x to both sides. 10y = –1(x + 4) 10y = –x – 4 x + 10y = –4 continued