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The Equation of a Line Three Forms of an Equation of a Line Gradient/Slope-Intercept Form: This form is useful for graphing, as the slope and the yintercept are readily visible. Point-Slope Form: The point-slope form allows you to use ANY point, together with the slope, to form the equation of the line. Standard /General Form: Note: a, b, and c are constants. 3

Point-Slope Form: 4

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The Equation of a Line Slope-Intercept Form– requires the y-intercept and the slope of the line. m = slope of line b = y-intercept 8

The Equation of a Line Slope-Intercept Form– requires the y-intercept and the slope of the line. m = slope of line b = y-intercept 9

The Equation of a Line Slope-Intercept Form– requires the y-intercept and the slope of the line. m = slope of line b = y-intercept 10

3. 3 – The Equation of a Line Slope-Intercept Form– requires the y-intercept and the slope of the line. m = slope of line b = y-intercept 11

The Equation of a Line Write an equation of a line given the slope and the y-intercept. 12

The Equation of a Line Point-Slope Form – requires the coordinates of a point on the line and the slope of the line. 13

The Equation of a Line Point-Slope Form – requires the coordinates of a point on the line and the slope of the line. 14

The Equation of a Line Point-Slope Form – requires the coordinates of a point on the line and the slope of the line. 15

The Equation of a Line Writing an Equation Given Two Points 1. Calculate the slope of the line. 2. Select the form of the equation. a. Standard form b. Slope-intercept form c. Point-slope form 3. Substitute and/or solve for the selected form. 16

The Equation of a Line Writing an Equation Given Two Points Given the two ordered pairs, write the equation of the line using all three forms. Calculate the slope. or 17

The Equation of a Line Writing an Equation Given Two Points Point-slope form 18

The Equation of a Line Writing an Equation Given Two Points Slope-intercept form 19

The Equation of a Line Writing an Equation Given Two Points Standard form LCD: 4 20

The Equation of a Line Solving Problems 21

3. 3 – The Equation of a Line Solving Problems The pool Entertainment company learned that by pricing a pool toy at $10, local sales will reach 200 a week. Lowering the price to $9 will cause sales to rise to 250 a week. a. Assume that the relationship between sales price and number of toys sold is linear. Write an equation that describes the relationship in slope-intercept form. Use ordered pairs of the form (sales price, number sold). b. Predict the weekly sales of the toy if the price is $7. 50. 22

The Equation of a Line Solving Problems 23

The Equation of a Line Solving Problems Predict the weekly sales of the toy if the price is $7. 50. 24

Linear Inequalities in Two Variables Are the ordered pairs a solution to the problem? 25

Linear Inequalities in Two Variables Are the ordered pairs a solution to the problem? true false true . The shaded region represents the solution set for the inequality. 26

Linear Inequalities in Two Variables Graph the solution set of the linear inequality false true 27

Linear Inequalities in Two Variables Graph the solution set of the linear inequality false true 28

Linear Inequalities in Two Variables Graph the solution set of the linear inequality false true 29

Linear Inequalities in Two Variables Graph the solution set of the linear inequality true false 30