1. ALGEBRA 1 Lesson 5-2 Warm-Up

2. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a line) which include the slope of the line and its y-intercept (where the line crosses the y-axis) – It is written as: where m (the coefficient of the x term) is the slope and b is the y- intercept (where the line crosses the y-axis)

3. ALGEBRA 1 The slope is 2 and the y-intercept is –3. What are the slope and y-intercept of y = 2x – 3? mx + b y = 2x – 3 Use the Slope-Intercept form. y = Slope-Intercept Form LESSON 5-2 Additional Examples

4. ALGEBRA 1 Write an equation of the line with slope and y-intercept 4. 2525 Use the slope-intercept form. y = mx + b y = x + 4 2525 2525 Substitute for m and 4 for b. Slope-Intercept Form LESSON 5-2 Additional Examples

5. ALGEBRA 1 y = mx + b Step 2 Write an equation in slope–intercept form. The y-intercept is 1. Write an equation for the line. Step 1 Find the slope. Two points on the line are (0, 1) and (3, –1). –1 – 1 3 – 0 slope = = – 2323 2323 y = – x + 1 Substitute – for m and 1 for b. 2323 Slope-Intercept Form LESSON 5-2 Additional Examples

6. ALGEBRA 1 “Slope-Intercept Form” (5-2) How can you determine if a point lies on the line of an equation? Every point that lies on the graph of an equation must make the equation true. Therefore, to verify (check) whether a point lies on a line, substitute the x and y values of the equation for the x and y coordinates of the point. If the result is a true statement (both sides equal one another), the point is a solution for that equation (in other words, it is part of the graph of that equation). Example:

7. ALGEBRA 1 Determine whether (1, 2) lies on the graph of y = 3x – 1. y = 3x – 1 2 3(1) – 1 Substitute 1 for x and 2 for y. 2 3 – 1 Multiply. 2 = 2Subtract. (1, 2) is a solution. Slope-Intercept Form LESSON 5-2 Additional Examples

8. ALGEBRA 1 “Slope-Intercept Form” (5-2) How do you graph an equation. There are two ways to graph an equation. Method 1: Slope-Intercept Form – y = mx + b Step 1: Start at the y-intercept (0, b) Step 2: Create a chain of stair-step of the rise (units up or down) and run (units to the right – never to the left since negative slopes go down not left). Place a dot after each step. Step 3: Connect the dots with a line. Method 2: Function Table Step 1: Create a table consisting of 3 colums and at least 3 rows. Label each column “x”, “(equation)”, and “y” Step 2: Create your own x values and place them in the “x” column (one per row). Tip: Use easy x values to substitute, like 0, 1, 2, -1, and -2. Step 3: Plot each (x, y) pair. Step 4: Connect the dots with a line.

9. ALGEBRA 1 “Slope-Intercept Form” (5-2) Example: Graph y = -2x + 1. Method 1: Slope-Intercept Form Step 1: The y-intercept is 1, so start at (0,1) Step 2: The slope is -2 or -2/1 which means a rise of -2 (down 2) and a run of 1 (right 1). Create a few stair-steps that go down 2 and right 1. Step 3: Connect the dots with a line.

10. ALGEBRA 1 “Slope-Intercept Form” (5-2) Example: Graph y = -2x + 1. Method 2: Function Table

11. ALGEBRA 1 The base pay for a used car salesperson is $300 per week. The salesperson also earns 15% commission on sales made. The equation t = 300 + 0.15s relates total earnings t to sales s. Graph the equation. Step 1 Identify the slope and y-intercept. t = 300 + 0.15s t = 0.15s + 300 Rewrite the equation in slope intercept form. slope y-intercept Slope-Intercept Form LESSON 5-2 Additional Examples

12. ALGEBRA 1 Step 2 Plot two points. First plot a point at the y-intercept. Then use the slope to plot a second point. (continued) Step 3 Draw a line through the points. 15 100 The slope is 0.15, which equals. Plot a second point 15 units above and 100 units to the right of the y-intercept. Slope-Intercept Form LESSON 5-2 Additional Examples

13. ALGEBRA 1 m = –2; b = 0 y = 0.5x + 1 3434 3535 m = ; b = –3 3434 y = – x – 4 3535 Find the slope and y-intercept of each equation. 1. y = x – 3 2. y = –2x Write an equation of a line with the given slope and y-intercept. 3. m = –, b = –4 4. m = 0.5, b = 1 Slope-Intercept Form LESSON 5-2 Lesson Quiz

14. ALGEBRA 1 5. Write an equation for the line. 6. Graph y = –x + 3. y = x – 3 1212 7. Determine whether (3, –7) lies on the graph of y = 4x – 5. (3, –7) is not a solution Slope-Intercept Form LESSON 5-2 Lesson Quiz