Today’s objective: To graph linear equations in slope intercept form Lesson 6-2-(part 1) Writing Equations in Slope-Intercept Form & Graphing Lines (page 291) Today’s objective: To graph linear equations in slope intercept form

Real-World Connection This skill can be used for relating total earnings to sales. (See Example 5.)

Vocabulary Linear equation – an equation whose graph is a line. y-intercept – the y-coordinate of the point where a line crosses the y-axis. Slope-intercept form – y = mx + b where m = slope and b = y-intercept.

Slope-Intercept Form What are the slope and y-intercept of y = 2x – 3? mx + b = 2x – 3 Use the Slope-Intercept form. The slope is 2; the y-intercept is –3. 6-2

Example 1, page 292 Find the slope and y-intercept of each equation. A) y = -2x + 1 B) y = (7/6)x – 3/4 C) y = -(4/5)x

Graphing Lines using the Slope and y-intercept Plot the y-intercept. From this point, use the slope and rise/run to plot a second point. Repeat step 2 to get a third point. Draw a line through the three points.

Slope-Intercept Form Graph y = x – 2. Step 2 1 3 Step 2 The slope is . Use slope to plot a second point. 1 3 Step 3 Draw a line through the two points. Step 1 The y-intercept is –2. So plot a point at (0,–2). 6-2

Example 4: GRAPH y= 3x - 1 y = 3/2 x - 2 y x 10 -10 y x 10 -10

y = -2x + 1 y = -2/3 x + 3 y x 10 -10 y x 10 -10

y = -2x y – 9x = 1/2 y x 10 -10 y x 10 -10

y – 2 = -3x y x 10 -10 y x 10 -10

Slope-Intercept Form 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 equations. 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 6-2

Slope-Intercept Form (continued) Step 2  Plot two points. First plot a point at the y-intercept. Then use the slope to plot a second point. The slope is 0.15, which equals . Plot a second point 15 units above and 100 units to the right of the y-intercept. 15 100 Step 3  Draw a line through the points. 6-2

Example 5, page 293 Suppose the base pay of the delivery person is $150 and his commission on each sale is 30%. The equation relating his total earnings t to sales s is t = 150 + 0.3s. Graph the equation. y x 2

Summary What did you learn today?

Summary What is the y-intercept? What is the slope intercept form of an equation? What does m represent? What does b represent? How can we graph a line using the slope and y-intercept?

ASSIGNMENT page 294 #1-9 all 28-40 all 41 - 67odd