Objective: Write an equation of a line in slope- intercept form given the slope and one point or two points.

Write an Equation given the Slope and a Point Remember that the slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept. You need to know both m and b in order to write an equation in slope-intercept form.

Example 1 Write an equation of a line that passes through (2, -3) with a slope of ½. In this problem, you are given m, but you must find b. m = ½ x = 2 y = -3 y = mx + b -3 = ½ (2) + b -3 = 1 + b -4 = b y = ½ x – 4

Write an Equation Given Two Points If you are given two points through which a line passes, you can use them to find the slope first. Remember that the formula for slope is Once you have the slope, use that slope and one of the points to find the y-intercept.

Example 2 Write an equation of the line that passes through each pair of points. a. (-3, -4) and (-2, -8) x 1 y 1 x 2 y 2 = -4 y = mx + b -4 = -4(-3) + b -4 = 12 + b = b m = -4 x = -3 y = -4 y = -4x – 16

Example 2 Write an equation of the line that passes through each pair of points. b. (6, -2) and (3, 4) x 1 y 1 x 2 y 2 = -2 y = mx + b -2 = -2(6) + b -2 = b = b m = -2 x = 6 y = -2 y = -2x + 10

Example 3 During one year, Malik’s cost for self-serve regular gasoline was $3.20 on the first of June and $3.42 on the first of July. Write a linear equation to predict Malik’s cost of gasoline the first of any month during the year, using 1 to represent January. (6, 3.20) and (7, 3.42) x 1 y 1 x 2 y 2 = 0.22 m = 0.22 x = 6 y = 3.20 y = mx + b 3.20 = 0.22(6) + b 3.20 = b = b y = 0.22x

Write and Use an Equation You can use a linear equation to make predictions about values that are beyond the range of the data. This process is called linear extrapolation.

Example 4 On average, Malik uses 25 gallons of gasoline per month. He budgeted $100 for gasoline in October. Use the prediction equation in Example 3 to determine if Malik will have to add to his budget. Explain. y = 0.22x For October, let x = 10. y = 0.22(10) y = y = 4.08 In October, each gallon will cost $ gallons $4.08 per gallon = $102 Malik will not have enough money. He will be short by $2.

Check Your Progress Choose the best answer for the following. Write an equation of a line that passes through (1, 4) and has a slope of -3. A. y = -3x + 4 B. y = -3x + 1 C. y = -3x + 13 D. y = -3x + 7 y = mx + b m = -3 x = 1 y = 4 4 = -3(1) + b 4 = -3 + b +3 7 = b

Check Your Progress Choose the best answer for the following. A. The table of ordered pairs shows the coordinates of two points on the graph of a line. Which equation describes the line? A. y = -x + 4 B. y = x + 4 C. y = x – 4 D. y = -x – 4 XY 3 26 x1x2x1x2 y1y2y1y2 = 1 m = 1 x = -1 y = 3 y = mx + b 3 = 1(-1) + b 3 = -1 + b +1 4 = b

Check Your Progress Choose the best answer for the following. B. Write the equation of the line that passes through the points (-2, -1) and (3, 14). A. y = 3x + 4 B. y = 5x + 3 C. y = 3x – 5 D. y = 3x + 5 x 1 y 1 x 2 y 2 = 3 m = 3 x = -2 y = -1 y = mx + b -1 = 3(-2) + b -1 = -6 + b +6 5 = b

Check Your Progress Choose the best answer for the following. The cost of a textbook that Mrs. Lambert uses in her class was $57.65 in She ordered more books in 2008 and the price increased to $ Write a linear equation to estimate the cost of a textbook in any year since Let x represent years since A. y = 3.5x B. y = 3.5x C. y = 57.65x D. y = -3.5x – 10 (0, 57.65) and (3, 68.15) x 1 y 1 x 2 y 2 = 3.5 m = 3.5 x = 0 y = y = mx + b = 3.5(0) + b = 0 + b = b

Check Your Progress Choose the best answer for the following. Mrs. Lambert needs to replace an average of 5 textbooks each year. Use the prediction equation from the last problem, where x is the years since 2005 and y is the cost of a textbook, to determine the cost of replacing 5 textbooks in A. $71.65 B. $ C. $ D. $ y = 3.5x For 2009, let x = 4. y = 3.5(4) y = y = In 2009, each book will cost $ books $71.65 per book