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• A surveys ask high school freshman whether they would be willing to pay $5 for their yearbooks. Out of the 225 freshman surveyed, 198 said “yes”. What percent of the freshman said “yes”? 88% Objective The student will be able to: 1) Graph linear equations in slope- intercept form. 2) write equations using slope-intercept form. 3) identify slope and y-intercept from an equation. Review Part Two Finding Slope without Graphing When you are given two points you may have to find the slope... Point A (2,-3) Point B (3,4) change in y slope change in x …without graphing. A B Find the slope when you are given two points from a line. Point A (2,-3) Point B (3,4) Use the formula for slope. Remember, m=slope. y2 y1 m x2 x1 Find the slope when you are given two points from a line. Point 1 (2,-3) Point 2 (3,4) y2 y1 m x2 x1 Use the formula for slope. Remember, m=slope. 4 3 m 3 2 7 m 7 1 Using the same points, but labeling them #2 and #1 Point 2 (2,-3) Point 1 (3,4) y2 y1 m x2 x1 Use the formula for slope. 3 4 m 23 Remember, m=slope. 7 m 7 1 Find the slope when you are given the following two points from a line. Point C (-2,-6) Point D (3,5) y2 y1 m x2 x1 Use the formula for slope. Remember, m=slope. 5 6 m 3 2 11 m 5 Find the slope when you are given the following two points from a line. Point E (9,6) Point F (1,4) Use the formula for slope. y2 y1 m x2 x1 46 m 1 9 Remember, m=slope. 2 1 m 8 4 Remember FORMULA FOR FINDING SLOPE The formula is used when you know two points of a line. They look like A( X1 , Y1 ) and B( X 2 , Y2 ) RISE Y2 Y1 SLOPE RUN X 2 X 1 EXAMPLE Find the slope of the line between the two points (-4, 8) and (10, -4) If it helps label the points. X1 Y1 X2 Y2 Then use the formula Y2 Y1 (4 (8) X 2 X 1 SUBSTITUTE INTO FORMULA (10) (4) (4) (8) 4 (8) 12 6 Then Simplify (10) (4) 10 4 14 7 Graphing Linear Equations In Slope-Intercept Form We have already seen that linear equations have two variables and when we plot all the (x,y) pairs that make the equation true we get a line. In this section, instead of making a table, evaluating y for each x, plotting the points and making a line, we will use The Slope-Intercept Form of the equation to graph the line. These equations are all in SlopeIntercept Form: y 2x 1 y x 4 3 y x2 2 Notice that these equations are all solved for y. Just by looking at an equation in this form, we can draw the line (no tables). •The constant is the y-intercept. •The coefficient is the slope. y 2x 1 Constant = 1, y-intercept = 1. y x 4 Constant = -4, y-intercept = -4. 3 y x2 2 Coefficient = 2, slope = 2. Coefficient = -1, slope = -1. Constant = -2, y-intercept = -2. Coefficient = 3/2, slope = 3/2. The formula for Slope-Intercept Form is: y mx b; • ‘b’ is the y-intercept. • ‘m’ is the slope. On the next three slides we will graph the three equations: 3 y 2x 1, y x 4, y x 2 2 using their y-intercepts and slopes. y 2x 1 right 1 right 1 up 2 up 2 1) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the yintercept = 1. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 2, so the slope = 2/1. y x 4 1) Plot the y-intercept as a point on the y-axis. The constant, b = -4, so the yintercept = -4. down 1 right 1 down 1 right 1 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -1, so the slope = -1/1. 3 y x2 2 right 2 up 3 right 2 up 3 1) Plot the y-intercept as a point on the y-axis. The constant, b = -2, so the yintercept = -2. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 3/2, so the slope = 3/2. Sometimes we must solve the equation for y before we can graph it. 2x y 3 2x y (2x) (2x) 3 y 2x 3 The constant, b = 3 is the y-intercept. The coefficient, m = -2 is the slope. y 2x 3 1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the yintercept = 3. down 2 right 1 down 2 right 1 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1. Important!!! This is one of the big concepts in Algebra 1. You need to thoroughly understand this! Slope – Intercept Form y = mx + b m represents the slope b represents the y-intercept Writing Equations When asked to write an equation, you need to know two things – slope (m) and y-intercept (b). There are three types of problems you will face. Writing Equations – Type #1 Write an equation in slope-intercept form of the line that has a slope of 2 and a y-intercept of 6. To write an equation, you need two things: slope (m) = 2 y – intercept (b) = 6 We have both!! Plug them into slope-intercept form y = mx + b y = 2x + 6 Write the equation of a line that has a y-intercept of -3 and a slope of -4. 1. y = -3x – 4 2. y = -4x – 3 3. y = -3x + 4 4. y = -4x + 3 Writing Equations – Type #2 Write an equation of the line that has a slope of 3 and goes through the point (2,1). To write an equation, you need two things: slope (m) = 3 y – intercept (b) = ??? We have to find the y-intercept!! Plug in the slope and ordered pair into y = mx + b 1 = 3(2) + b Writing Equations – Type #2 1 = 3(2) + b Solve the equation for b 1=6+b -6 -6 -5 = b To write an equation, you need two things: slope (m) = 3 y – intercept (b) = -5 y = 3x - 5 Writing Equations – Type #3 Write an equation of the line that goes through the points (-2, 1) and (4, 2). To write an equation, you need two things: slope (m) = ??? y – intercept (b) = ??? We need both!! First, we have to find the slope. Plug the points into the slope formula. 2 1 m 4 (2) 1 Simplify m 6 Writing Equations – Type #3 Write an equation of the line that goes through the points (-2, 1) and (4, 2). To write an equation, you need two things: 1 slope (m) = 6 y – intercept (b) = ??? It’s now a Type #2 problem. Pick one of the ordered pairs to plug into the equation. Which one looks easiest to use? I’m using (4, 2) because both numbers are positive. 1 2 = (4) + b 6 Writing Equations – Type #3 1 2 = (4) + b 6 Solve the equation for b 2 2= +b 3 2 2 3 3 1 1 b 3 To write an equation, you need two things: 1 slope (m) = 6 1 y y – intercept (b) = 1 3 1 1 x 1 6 3 Write an equation of the line that goes through the points (0, 1) and (1, 4). 1. 2. 3. 4. y = 3x + 4 y = 3x + 1 y = -3x + 4 y = -3x + 1 To find the slope and y-intercept of an equation, write the equation in slope-intercept form: y = mx + b. Find the slope and y-intercept. 1) y = 3x – 7 y = mx + b m = 3, b = -7 Find the slope and y-intercept. 2 2) y = x 3 y = mx + b 2 y= x+0 2 m= 3 b=0 3 3) y = 5 y = mx + b y = 0x + 5 m=0 b=5 Find the slope and y-intercept. 4) 5x - 3y = 6 Write it in slope-intercept form. (y = mx + b) 5x – 3y = 6 -3y = -5x + 6 -3 -3 -3 y= 5 3 x-2 5 m= 3 b = -2 Find the slope and y-intercept. 5) 2y + 2 = 4x Write it in slope-intercept form. (y = mx + b) 2y + 2 = 4x 2y = 4x - 2 2 2 2 y = 2x - 1 m=2 b = -1 Find the slope and y-intercept of y = -2x + 4 1. 2. 3. 4. m = 2; b = 4 m = 4; b = 2 m = -2; b = 4 m = 4; b = -2 Home Education!!! • Section 4.5 pg.247-248 #4-16(EVEN), 17-19, 26, 28, 30, 33, 40 Next class Quiz #5 Sec. 4.3 & 4.4!