1. Equations in Slope- Intercept Form Honors Math – Grade 8

2. Get Ready for the Lesson An online store charges $3 per book plus $0.99 per book for shipping. Take a look at the table and graph below. The shipping cost can be represented by the direct variation equation y = 0.99x where x represents the number of books. The slope of the line is 0.99. A point on the line is (0,3). Write an equation of the line

3. KEY CONCEPT Slope-Intercept Form The linear equation y = mx + b is in slope-intercept form, where m is the slope and b is the y-intercept. y = mx + b

4. Write an equation of the line in slope-intercept form that has the given slope and the given y-intercept. The slope is 3 and the y-intercept is -5. Substitute 3for m, and -5 for b. Simplify. The slope is – ½ and the y-intercept is 3. Substitute –½ for m, and 3 for b.

5. Write an equation in slope-intercept form of the line shown in the graph. The line crosses the y-axis at (0, 3). The y-intercept is 3. Find the slope. Write the equation. Substitute -2 for m and 3 for b. Locate two points on the line. (0, -1) and (4, 0) The line crosses the y-axis at (0, -1). The y-intercept is -1. Find the slope. Write the equation. Substitute 1/4 for m and -1 for b. Simplify

6. Graph each equation. The equation is in slope intercept form. The slope is – 2/3 & the y-intercept is 1. Step 1. Graph the y-intercept. (0, 1). Step 2. Use the slope to find another point on the line. Move down 2 units (for the rise) and then right 3 units (for the run). Plot the point. Step 3. Connect the points with a smooth line.

7. Graph each equation. This equation is not in slope-intercept form. Write it in slope-intercept form by solving for y The slope is 5/3 & the y-intercept is -2. Step 1. Graph the y-intercept. (0, -2). Step 2. Use the slope to find another point on the line. Move up 5 units (for the rise) and then right 3 units (for the run). Plot the point. Step 3. Connect the points with a smooth line. Divide all terms by -3.

8. In 1997, 2.6 million girls competed in high school sports. The number of girls competing in high school sports has increased by an average of 0.06 million per year since 1997. Write a linear equation to find the number of girls in high school sports in any year after 1997. Define the variables. Let G = # of girls competing. Let n = # of years after 1997. Write an equation. G= Rate of Change x Years after 1997 + Number at start This represents a linear equation in slope-intercept form. Find the number of girls competing in 2007. Since 2007 is 10 years after 1997, n = 10. Substitute n = 10 into the linear equation and solve. In 2007, 3.2 million girls competed in high school sports.