4.5 quick graphs using slope-intercept form, pointslope form, & standard form Algebra 1 Objectives Graph a line given any linear equation. Understand and use slopeintercept form. Understand and use the standard form of an equation. Understand and use point-slope form of an equation. We have used 3 different methods for graphing equations. 1) Using slope-intercept form. 2) Using x- and y-intercepts. 3) Using point-slope form. What form is used to graph x- and yintercepts? The goal is to determine which method is the easiest to use for each problem! Various Forms of an Equation y mx b of a Line. Slope-Intercept Form Standard Form m slope of the line b y intercept Ax By C A, B, and C are integers A 0, A must be postive y y1 m x x1 Point-Slope Form m slope of the line x1 , y1 is any point Here’s your cheat sheet: If the equation is in STANDARD FORM, graph using the intercepts. If the equation is in SLOPE-INTERCEPT FORM, graph using slope and intercept or a t-table (whichever is easier for you). If the equation is in neither form, choose the method you like the best! 6 4.5 Slope Intercept Form TELEPHONE COSTS In a community, the monthly cost of local telephone service is $5 per month, plus 25¢ per call. a. Write a linear equation that gives the cost c for a. person making n calls. b. Then graph the equation. (need 2 points) c. Use the graph to estimate the cost of service in a month when 20 calls were made. c = 5 + .25n Slope-Intercept Form y = mx + b slope rise run y-intercept where the line crosses the y axis Slope-Intercept Form: A linear equation written in the form y = mx + b is in slope-intercept form. The slope is m and the y-intercept is (0, b). To graph an equation in slope-intercept form: 1. Write the equation in the form y = mx + b. Identify m and b. 2. Plot the y-intercept (0, b). 3. Starting at the y-intercept, find another point on the line using the slope. 4. Draw the line through (0, b) and the point located using the slope. 9 Slope-Intercept Form Example: Graph the line y = 2x – 4. 1. The equation y = 2x – 4 is in the slope-intercept form. So, m = 2 and b = - 4. y 2. Plot the y-intercept, (0, - 4). 3. The slope is 2. m = change in y change in x x 2 = 1 (1, -2) 2 4. Start at the point (0, 4). Count 1 unit to the right and 2 units up to locate a second point on the line. The point (1, -2) is also on the line. 5. Draw the line through (0, 4) and (1, -2). (0, - 4) 1 Which graphing method is easiest? Since the equation is already in slopeintercept form, use slope and the yintercept! Graph using m and b 1 m= ,b=2 3 2. Graph -2x + 3y = 12 Which graphing method is easiest? Using x- and y-intercepts! (The equation is in standard form) Remember, plug in 0 to find the intercepts. Standard Form: Graphing with intercepts: -2x + 3y = 12 1. 2. Find your x-intercept: Let y = 0 -2x + 3(0) = 12 x = -6; (-6, 0) Find your y-intercept: Let x = 0 -2(0) + 3y = 12 y = 4; (0, 4) Graph both points and draw a line through them. Which method is easiest to graph -3x + 6y = 2? 1. 2. 3. 4. T-table Slope and intercept X- and Y-intercepts Graphing calculator Explain. 14 Point-Slope Form: A linear equation written in the form y – y1 = m(x – x1) is in point-slope form. The graph of this equation is a line with slope m passing through the point (x1, y1). y Example: The graph of the equation y – 3 = - 1 (x – 4) is a line 2 1 8 m=4 of slope m = - passing 1 2 (4, 3) 2 through the point (4, 3). x 4 8 15 Point-Slope Form Write the slope-intercept form for the equation of the line through the points (4, 3) and (-2, 5). m= 5–3 =- 2 =- 1 -2 – 4 6 3 Calculate the slope. y – y1 = m(x – x1) Point-slope form 1 y – 3 = - (x – 4) 3 y = - 1 x + 13 3 3 1 Use m = - and the point (4, 3). 3 Slope-intercept form 16 Point-Slope Form Example: Write the slope-intercept form for the equation of the line through the point (-2, 5) with a slope of 3. Use the point-slope form, y – y1 = m(x – x1), with m = 3 and (x1, y1) = (-2, 5). y – y1 = m(x – x1) Point-slope form y – y1 = 3(x – x1) Let m = 3. y – 5 = 3(x – (-2)) Let (x1, y1) = (-2, 5). y – 5 = 3(x + 2) Simplify. y = 3x + 11 Slope-intercept form Which is the graph of y = x + 2? 1. . 2. . 3. . 4. . 1. On the next few slides are some practice problems. 2. Choose which method is easiest first. Then solve and graph the equation. 3. Let’s Graph the following equations y 3x 2 2x 3 y 0 4x y 5 7x 3y 4 1 y 3 x 4 5x 2 y 2 x 3 y 12 yx3 y 6 x y 2x 1 We have used 3 different methods for graphing equations. 1) Using slope-intercept form. 2) Using x- and y-intercepts. 3) Using point-slope form. What form is used to graph xand y-intercepts? What form is used when the slope is given with one point? Linear Equation Review: Slope-Intercept Form Standard Form y mx b m slope of the line b y intercept Ax By C A, B, and C are integers A 0, A must be postive y y1 m x x1 Point-Slope Form m slope of the line x1 , y1 is any point Chapter 4 Test Wednesday, November 20th Chapter 4 Test Review Tuesday, November 19th Chapter 4 Study Guide due Tuesday, November 19th