8 5 PointSlope Form Warm Up Problem of
8 -5 Point-Slope Form Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
8 -5 Point-Slope Form Warm Up Write the equation of the line that passes through each pair of points in slope-intercept form. 1. (0, – 3) and (2, – 3) 2. (5, – 3) and (5, 1) 3. (– 6, 0) and (0, – 2) 4. (4, 6) and (– 2, 0) y = – 3 x=5 y = – 1 x – 2 3 y=x+2
8 -5 Point-Slope Form Problem of the Day Without using equations for horizontal or vertical lines, write the equations of four lines that form a square. Possible answer: y = x + 2, y = x – 2, y = –x + 2, y = –x – 2
8 -5 Point-Slope Form Sunshine State Standards MA. 8. A. 1. 1 Create…models to represent, analyze, and solve problems related to linear equations.
8 -5 Point-Slope Form Vocabulary point-slope form
8 -5 Point-Slope Form The point-slope form of an equation of a line with slope m passing through (x 1, y 1) is y – y 1 = m(x – x 1). Point on the line (x 1 , y 1 ) Point-slope form y – y 1 = m ( x – x 1) slope
8 -5 Point-Slope Form Additional Example 1 A: Using Point-Slope Form to Identify Information About a Line Use the point-slope form of each equation to identify a point the line passes through and the slope of the line. y – 7 = 3(x – 4) y – y 1 = m(x – x 1) The equation is in point-slope y – 7 = 3(x – 4) form. Read the value of m from the m=3 equation. (x 1, y 1) = (4, 7) Read the point from the equation. The line defined by y – 7 = 3(x – 4) has slope 3, and passes through the point (4, 7).
8 -5 Point-Slope Form Additional Example 1 B: Using Point-Slope Form to Identify Information About a Line y– 1=1 3(x + 6) y – y 1 = m(x – x 1) y – 1 = 1 (x + 6) 3 Rewrite using subtraction y – 1 =1 [x – (– 6)] 3 instead of addition. m =1 3 (x 1, y 1) = (– 6, 1) The line defined by y – 1 = 1 (x + 6) has slope 1 , and 3 3 passes through the point (– 6, 1).
8 -5 Point-Slope Form Check It Out: Example 1 A Use the point-slope form of the equation to identify a point the line passes through and the slope of the line. y– 2=2 3(x + 3) 2 y – 2 = (x –(– 3)) 3 m =2 3 (x 1, y 1) = (– 3, 2)
8 -5 Point-Slope Form Check It Out: Example 1 B Use the point-slope form of the equation to identify a point the line passes through and the slope of the line. y + 5 = 2(x – 1) y –(– 5) = 2(x – 1) m=2 (x 1, y 1) = (1, – 5)
8 -5 Point-Slope Form Additional Example 2 A: Writing the Point-Slope Form of an Equation Write the point-slope form of the equation with the given slope that passes through the indicated point. the line with slope 4 passing through (5, – 2) y – y 1 = m(x – x 1) [y – (– 2)] = 4(x – 5) y + 2 = 4(x – 5) Substitute 5 for x 1, – 2 for y 1, and 4 for m. The equation of the line with slope 4 that passes through (5, – 2) in point-slope form is y + 2 = 4(x – 5).
8 -5 Point-Slope Form Additional Example 2 B: Writing the Point-Slope Form of an Equation the line with slope – 5 passing through (– 3, 7) y – y 1 = m(x – x 1) y – 7 = – 5[x – (– 3)] Substitute – 3 for x 1, 7 for y 1, and – 5 for m. y – 7 = – 5(x + 3) The equation of the line with slope – 5 that passes through (– 3, 7) in point-slope form is y – 7 = – 5(x + 3).
8 -5 Point-Slope Form Check It Out: Example 2 A Write the point-slope form of the equation with the given slope that passes through the indicated point. the line with slope 2 passing through (2, – 2) y – y 1 = m(x – x 1) y – (– 2) = 2(x – 2) y + 2 = 2(x – 2)
8 -5 Point-Slope Form Check It Out: Example 2 B the line with slope 1 passing through (– 3, 2) 4 y – y 1 = m(x – x 1) y – 2 = 1 (x – (– 3)) 4 y – 2 = 1 (x + 3) 4
8 -5 Point-Slope Form Additional Example 3: Entertainment Application A roller coaster starts by ascending 20 feet for every 30 feet it moves forward. The coaster starts at a point 18 feet above the ground. Write the equation of the line that the roller coaster travels along in point-slope form, and use it to determine the height of the coaster after traveling 150 feet forward. Assume that the roller coaster travels in a straight line for the first 150 feet. As x increases by 30, y increases by 20, so the slope 2 of the line is 20 or. The line passes through the 30 3 point (0, 18).
8 -5 Point-Slope Form Additional Example 3 Continued y – y 1 = m(x – x 1) Substitute 0 for x 1, 18 for y 1, y – 18 = 2 (x – 0) 3 and 2 for m. 3 The equation of the line the roller coaster travels along, in point-slope form, is y – 18 = 2 x. Substitute 150 for x 3 to find the value of y. y – 18 = 2 (150) 3 y – 18 = 100 y = 118 The value of y is 118, so the roller coaster will be at a height of 118 feet after traveling 150 feet forward.
8 -5 Point-Slope Form Check It Out: Example 3 At sea level, the boiling point of water is 212°F. The boiling point decreases 1°F for every 500 ft of increase in altitude. Write an equation for the boiling point of water in point -slope form, and use it to find the boiling point of water at 6000 ft above sea level. (0, 212); rate of change is – 1°F so m = – 1 500 +500 ft y – 212 = – 1 (x – 0) 500 y – 212 = – 1 (6000), or y = 200 500 200 °F
8 -5 Point-Slope Form Lesson Quizzes Standard Lesson Quiz for Student Response Systems
8 -5 Point-Slope Form Lesson Quiz Use the point-slope form of each equation to identify a point the line passes through and the slope of the line. 1. y + 6 = 2(x + 5) (– 5, – 6), 2 2. y – 4 = 2 – 5 (x 2 (6, 4), – – 6) 5 Write the point-slope form of the equation with the given slope that passes through the indicated point. 3. the line with slope 4 passing through (3, 5) y – 5 = 4(x – 3) 4. the line with slope – 2 passing through (– 2, 4) y – 4 = – 2(x + 2)
8 -5 Point-Slope Form Lesson Quiz for Student Response Systems 1. Use the point-slope form of the equation y + 4 = 5(x + 6) to identify a point the line passes through and the slope of the line. A. (– 6, – 4); 5 B. (– 6, – 4); – 5 C. (6, 4); 5 D. (6, 4); – 5
8 -5 Point-Slope Form Lesson Quiz for Student Response Systems 2. Identify the point-slope form of the equation of the line with slope 6 passing through the point (3, 1). A. y – 1 = – 6(x – 3) B. y + 1 = – 6(x + 3) C. y – 1 = – 6(x – 3) D. y + 1 = – 6(x + 3)
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