1. 2.4 Linear Functions: Graphs and Slopes

2. Slope is the steepness of the line (the slant of the line) and is defined by rise the change in y run the change in x y 2 – y 1 y 1 – y 2 x 2 – x 1 x 1 – x 2 m = = = or SLOPE IS ALSO CALLED AS THE RATE OF CHANGE

3. Find the slope of the line that goes through these 2 points 1)(1,5); (2,7) 2)(2,3); (1,3)

4. Slope – intercept form y = mx + b m is the slope, b is the y-intercept

5. Y –intercept shows whether the graph shifted up or down Example: Y = 2x slope is 2, y-intercept is ___ Y = 2x + 5 slope is 2, y-intercept is ___ Y = 2x – 3 slope is 2, y-intercept is ___

6. Find the slopes and the y-intercepts 1)y = ½ x + 4 Slope is ½ and y-intercept is 4 2)5x – 4y = 8 -4y = -5x + 8 y = 5/4 x - 2 Slope is 5/4 and y-intercept is -2

7. Find the linear equation if you know slope m = 3 and y-intercept is (0,4) We have y =mx + b So y = 3x + 4

8. Graphing using slopes and y- intercepts Start by plotting y-intercept (0,b) From there, use the slope = rise / run If +, go up, or right If -, go down or left

9. Y = 3x + 2 Step 1: Start with the y-intercept (0,2) Step 2: Slope is 3/1 so we rise 3 (up 3) and run 1 (to the right 1) Step 3: Connect 2 points, we will have the function y = 3x - 2

10. More problems 1)Y = (1/2)x – 3 2)Y = (-3/4)x + 1 3)Y = -2x - 2

12. More examples Writing functions 1)Open a new business with the initial cost is $100,000. Profit is $500 per day. Write the profit function for d number of days. 2)Bought a new car for $40,000. The value of the car depreciates at a rate of $100 per day. Write the value function for d number of days.