2.4 Linear Functions: Graphs and Slope

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 y2 – y1 y1 – y2 x2 – x1 x1 – x2 = m = = or SLOPE IS ALSO CALLED AS THE RATE OF CHANGE

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

Y –intercept shows whether the graph shifted up or down Example: Y = 2x Y = 2x + 5 Y = 2x – 3

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

Find the slopes and the y-intercepts y = ½ x + 4 5x – 4y = 8

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

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

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

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