5 7 SlopeIntercept Form Warm Up Problem of

5 -7 Slope-Intercept Form Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

5 -7 Slope-Intercept Form Warm Up Tell whether the slope is positive or negative. Then find the slope. negative; – 2 3

5 -7 Slope-Intercept Form Problem of the Day A cat weighs 11 ounces at birth. It gains 0. 5 ounces a day for the first two weeks. How much will the cat weigh at the end of two weeks? The cat will weigh 1 lb, 2 oz.

5 -7 Slope-Intercept Form Sunshine State Standards Preview of MA. 8. A. 1. 2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem.

5 -7 Slope-Intercept Form Vocabulary x-intercept y-intercept slope-intercept form

5 -7 Slope-Intercept Form The x-intercept of a line is the x-coordinate of the point where the line intersects the x-axis. The y-coordinate of this point is always 0. The y-intercept of a line is the y-coordinate of the point where the line intersects the y-axis. The x-coordinate of this point is always 0.

5 -7 Slope-Intercept Form Additional Example 1: Finding x- and y-intercepts Find the x- and y-intercepts. y A. The line intersects the x-axis at (2, 0). 4 2 x – 4 – 2 – 4 0 2 4 The x-intercept is 2. The line intersects the x-axis at (– 4). The y-intercept is – 4.

5 -7 Slope-Intercept Form Additional Example 1: Finding x-intercepts and y-intercepts to Graph Linear Equations Find the x- and y-intercepts. y B. The line intersects the x-axis at (4, 0). 4 2 x – 4 – 2 – 4 0 2 4 The x-intercept is 4. The line intersects the x-axis at (0, 1). The y-intercept is 1.

5 -7 Slope-Intercept Form Check It Out: Example 1 Find the x- and y-intercepts. A. y The line intersects the x-axis at (1, 0). 4 2 x – 4 – 2 – 4 0 2 4 The x-intercept is 1. The line intersects the x-axis at (– 3). The y-intercept is – 3.

5 -7 Slope-Intercept Form Check It Out: Example 1 Find the x- and y-intercepts. B. y The line intersects the x-axis at (5, 0). 4 2 x – 4 – 2 – 4 0 2 4 The x-intercept is 5. The line intersects the x-axis at (0, 2). The y-intercept is 2.

5 -7 Slope-Intercept Form The linear equation y = mx + b is written in slope-intercept form, where m is the slope and b is the y-intercept of the line. y = mx + b Slope y-intercept

5 -7 Slope-Intercept Form Additional Example 2 A: Graphing by Using Slope and y-intercept Graph the equation. 1 A. y = x + 1 3 Step 1: Find m and b. y= 1 x+1 3 m=1 3 b= 1 Step 2: Plot (0, 1) 1 Step 3: Use the slope to plot at least 1 3 more point on the line.

5 -7 Slope-Intercept Form Additional Example 2 A Continued Graph the equation. 1 y= x+1 3 y 4 2 x – 4 – 2 0 2 4 – 4 Step 4: Draw a line through the points.

5 -7 Slope-Intercept Form Remember! Since the y-intercept is 1, the point (0, 1) is a point on the line.

5 -7 Slope-Intercept Form Additional Example 2: Graphing by Using Slope and y-intercept Graph the equation. B. 3 x + y = 5 Step 1: Find m and b. 3 x + y = 5 – 3 x = – 3 x 3 x + y = 5 is not in the form y = mx+b, so solve for y. y = 5 – 3 x y = – 3 x + 5 m = – 3 b=5

5 -7 Slope-Intercept Form Additional Example 2 B Continued Step 2: Plot (0, 5) Step 3: Use the slope – 3 to plot at least 1 more point on the line. Step 4: Draw a line through the points.

5 -7 Slope-Intercept Form Check It Out: Example 2 A Graph the equation. 1 y= x+2 4 Step 1: Find m and b. y= 1 x+2 4 m=1 4 b= 2 Step 2: Plot (0, 2) 1 Step 3: Use the slope to plot at least 1 4 more point on the line.

5 -7 Slope-Intercept Form Check It Out: Example 2 A Continued Graph the equation. 1 y= x+2 4 y 4 2 x – 4 – 2 0 2 4 – 4 Step 4: Draw a line through the points.

5 -7 Slope-Intercept Form Check It Out: Example 2 B Graph the equation. 2 x + y = 4 Step 1: Find m and b. 2 x + y = 4 – 2 x = – 2 x 2 x + y = 4 is not in the form y = mx+b, so solve for y. y = 4 – 2 x y = – 2 x + 4 m = – 2 b=4

5 -7 Slope-Intercept Form Check It Out Example 2 B Continued Step 2: Plot (0, 4) Step 3: Use the slope – 2 to plot at least 1 more point on the line. Step 4: Draw a line through the points.

5 -7 Slope-Intercept Form Additional Example 3: Writing an Equation in Slope. Intercept Form Write the equation of the line in slope-intercept form. The line falls from left to right so the slope is negative. m = rise = - 2 5 run The line intersects the y-axis at (0, -4), so the y-intercept is -4. b = – 4 Substitute for m and b. y =– 2 x – 4 5

5 -7 Slope-Intercept Form Check It Out: Example 3 Write the equation of the line in slope-intercept form. The line rises from left to right so the slope is positive. m = rise = run 1 2 The line intersects the y-axis at (0, 2), so the y-intercept is 2. b=2 Substitute for m and b. y = 1 x + 2 2

5 -7 Slope-Intercept Form Additional Example 4: Using Slope-Intercept Form A spider descends a 20 -foot drainpipe at a rate of 2 feet per minute. The linear equation y = – 2 x + 20 represents the distance y the spider has left to descend after x minutes. Graph the equation, and then identify the x- and y- intercepts and describe their meaning.

5 -7 Slope-Intercept Form Use the slope and y-intercept to graph the equation. Plot (0, 20). Use the slope -2 to plot the line down to the x-axis. The y-intercept is 20. This represents the total distance in feet the spider has to descend. The x-intercept is 10. This represents the time in minutes it takes the spider has to descend the 20 ft. Distance remaining (ft) Additional Example 4 Continued Spider's Decent 20 18 16 14 12 10 8 6 4 2 2 4 6 8 10 12 14 16 Time (min)

5 -7 Slope-Intercept Form Check It Out: Example 4 A submarine descends into a 40 -mile sea cave at a rate of 5 miles per minute. The linear equation y = – 5 x + 40 represents the distance y the submarine has left to descend after x minutes. Graph the equation, and then identify the x- and y- intercepts and describe their meaning.

5 -7 Slope-Intercept Form Use the slope and y-intercept to graph the equation. Plot (0, 40). Use the slope -5 to plot the line down to the x-axis. The y-intercept is 40. This represents the total distance in feet the submarine has to descend. The x-intercept is 8. This represents the time in minutes it takes the submarine to descend the 40 miles. Distance remaining (mi) Check It Out: Example 4 Continued Submarine's Decent 45 40 35 30 25 20 15 10 5 1 2 3 4 5 6 7 8 9 Time (min)

5 -7 Slope-Intercept Form Lesson Quizzes Standard Lesson Quiz for Student Response Systems

5 -7 Slope-Intercept Form Lesson Quiz: Part I 3 1. Graph y = x – 3. Identify the x- and y 8 intercepts. y 8 4 x – 8 – 4 0 4 8 – 8 x-int. = 8, y-int. = – 3

5 -7 Slope-Intercept Form Lesson Quiz: Part II 2. Write the equation of the line in slopeintercept form. y 8 4 x – 8 – 4 0 4 – 8 1 y=– x+3 2 8

5 -7 Slope-Intercept Form Lesson Quiz 3. A snail is crawling across a 15 mm long leaf. The snail crawls at a constant rate of 1 mm per second. The linear equation y = –x + 15 represents the distance y that the snail has left to crawl after x seconds. Graph the equation, and then identify the x- and y-intercepts and describe their meanings. y-int. = 15, total distance in mm that the snail has to crawl; x-int. = 15, time in seconds it takes the snail to crawl 15 mm.

5 -7 Slope-Intercept Form Lesson Quiz for Student Response Systems 1. Graph y = – 3 x – 3. Identify the x- and 2 2. y-intercepts. A. x-int: – 2, y-int: – 3 B. x-int: 2, y-int: 3

5 -7 Slope-Intercept Form Lesson Quiz for Student Response Systems 2. Write the equation of the line in slopeintercept form. 2 A. y = x – 3 3 2 B. y = x + 2 3 3 C. y = x – 3 2 3 D. y = x + 2 2

5 -7 Slope-Intercept Form Lesson Quiz for Student Response Systems 3. A gelato shop charges $3 for a cup of gelato, plus $1. 50 for each topping. The equation C = 1. 5 t + 3 represents the cost of the cup of gelato for t number of toppings. Graph the equation, and then identify the x- and y -intercepts. A. x-int: 3, y-int: none B. x-int: none, y-int: 3