5-2 Slope Intercept Form Hubarth Algebra

Y-INTERCEPT- is the y-coordinate of the point where the line crosses the y-axis. The x-coordinate of the y-intercept is always 0, so the coordinates of the y-intercept will always be (0, y), y can be any real number. X-INTERCEPT- is the x-coordinate of the point where the line crosses the x-axis. The y-coordinate of the x-intercept is always 0, so the coordinates of the x-intercept will always be (x, 0), x can be any real number. Slope-Intercept Form The slope-intercept form of a linear equation is y = mx + b. m = the slope of the line. b = the y-intercept. (0, b)

Ex 1 Identifying Slope and Y-intercept What are the slope and y-intercept of y = 2x – 3? mx + b y = 2x – 3 Use the Slope-Intercept form. slope, m = 2 y-intercept, b = (0, -3)

Ex 2 Writing an Equations 5 Write an equation of the line with slope and y-intercept 4. Use the slope-intercept form. y = mx + b y = x + 4 2 5 Substitute for m and 4 for b.

Ex 3 Writing an Equation From a Graph 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 = = – 2 3 Step 2 Write an equation in slope–intercept form. The y-intercept is 1. y = mx + b 2 3 y = – x + 1 Substitute – for m and 1 for b.

Ex 4 Verifying a point on a Line 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 = 2 Subtract. (1, 2) is a solution.

Step 1 Identify the slope and y-intercept. t = 300 + 0.15s Ex 5 Graphing Equations 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 Step 2  Plot two points. First plot a point at the y-intercept. Then use the slope to plot a second point. 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. Step 3  Draw a line through the points.

. . Practice 1. Find the slope and y-intercept of each equation 2. Write the equation of the line given the slope and y-intercept.. 3. Write the equation of the line from the graph. . (0, 1) . (2, 2) 4. Determine whether the point lies on the line. a. (1, 6), y = 4x -2 b. (3, -5), y = -3x + 4 No Yes