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1.Use the given points to find the following: (8, 4) and ( 4, 5) a)Find the slope of the line that goes through the two points. 3 4 ( 4) ( 5) 8 4 – –

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Presentation on theme: "1.Use the given points to find the following: (8, 4) and ( 4, 5) a)Find the slope of the line that goes through the two points. 3 4 ( 4) ( 5) 8 4 – –"— Presentation transcript:

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2 1.Use the given points to find the following: (8, 4) and ( 4, 5) a)Find the slope of the line that goes through the two points. 3 4 ( 4) ( 5) 8 4 – – Simplify Reduce m = y 2 – y 1 x 2 – x 1 Formula m = m = m = m = Substitute © by S-Squared, Inc. All Rights Reserved.

3 1.Use the given points to find the following: (8, 4) and ( 4, 5) b)Find the y-intercept of the line that goes through the two points. Slope intercept form: y = mx + b Note: Substitute one of the given points and the calculated slope from part a into the slope intercept form of a linear equation to find b (the y-intercept). (4) = (8) + b 3 4 Substitute Simplify 4 = 6 + b Subtract – 6 2 = b y-intercept: (0, 2)

4 Use the given points to find the following: (8, 4) and ( 4, 5) c)Write the equation in slope-intercept form y-intercept: (0, 2) m = d)Graph: Slope Equation y = x – y-intercept 3 4 m = y-intercept: (0, 2) Slope – intercept form: y = mx + b

5 1.Use the given points to find the following: (8, 4) and ( 4, 5) e)Write the equation in function notation. y = x – f (x) = x – f ( 8) = ( 8) – Substitute Simplify f ( 8) = 6 – 2 f ( 8) = 8 f)Find f ( 8)

6 y = x m = 5 2.Given the following, write the equation of the line in slope-intercept form that passes through the given point and is: a) Parallel to the given line. (10, 5) y = x Note: Parallel lines have the same slope. Given point: (10, 5) Substitute Simplify 5 = (10) + b 2 5 – = 4 + b Subtract 1 = b Final Answer Slope – intercept form: y = mx + b Slope – intercept form: y = mx + b

7 5 m = 2 2.Given the following, write the equation of the line in slope-intercept form that passes through the given point and is: b) Perpendicular to the given line. (10, 5) y = x Note: Perpendicular lines have opposite reciprocal slopes. Given point: (10, 5) y = x + 30 Substitute Simplify 5 = (10) + b = 25 + b Add 30 = b Final Answer Slope – intercept form: y = mx + b Slope – intercept form: y = mx + b

8 y = x Given the following, write the equation of the line in slope-intercept form that passes through the given point as is: c) Write the given equation in standard form. (10, 5) y = x – 2x 2 5 Standard Form: Ax + By = C Where A, B, and C are integers Multiply each term by the LCD 5 5 ( ( ( 5 ( 5y = 2x x + 5y = 45 Subtract

9 3.A group of adults and children attend the premiere of the ballet. An adults ticket cost $14.00 each and a childs ticket cost $7.00 each. The total ticket sales equaled $ a) Write an equation that represents the possible number of adults and children who attended. Assign variables: Let, a = the number of adults who attended c = the number of children who attended Set equal to the total 14a + 7c = 420

10 3.A group of adults and children attend the premiere of the ballet. An adults ticket cost $14.00 each and a childs ticket cost $7.00 each. The total ticket sales equaled $ b) If 40 children attended, how many adults attended? 14a + 7c = 420 Notice: a = the # of adults who attended. c = the # of children who attended. Substitute 14a + 7(40) = 420 Let, c = 40 Simplify 14a = 420 Subtract – a = 140 Divide 14 a = adults attended

11 Slope – intercept form: y = mx + b Given the graph below, write the equation of the line in slope – intercept form : Identify the y-intercept: b = 4 Identify the slope: m = Substitute y = x


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