Chapter 5 Review PAY ATTENTION: SOME OF THESE QUESTIONS MAY BE ON THE TEST!! PAY ATTENTION: SOME OF THESE QUESTIONS MAY BE ON THE TEST!!

5.1 Slope  Find the slope of the line through the points  (4,9) and (1,6)  (-8,10) and (4,10)  (2,-30) and (2,12)  Determine the value of r.  (-1,-3) and (7,r) m = 3/4  (2,8) and (r,-4) m = -3  Find the slope of the line through the points  (4,9) and (1,6)  (-8,10) and (4,10)  (2,-30) and (2,12)  Determine the value of r.  (-1,-3) and (7,r) m = 3/4  (2,8) and (r,-4) m = -3

Slope as Rate of Change  The life expectancy of women born in 2000 was 74. The predicted life expectancy of women born in 2025 is 78. Find the rate of change.  In 1999, a daily newspaper had 12,125 subscribers. In 2004, it had 10,100 subscribers. Find the rate of change.  The life expectancy of women born in 2000 was 74. The predicted life expectancy of women born in 2025 is 78. Find the rate of change.  In 1999, a daily newspaper had 12,125 subscribers. In 2004, it had 10,100 subscribers. Find the rate of change.

Direct Variation  Remember y = kx where k is the constant of variation  The slope is the same as the constant of variation.  Find the direct variation equation and then solve.  If y = 4 when x = 2, find y when x = 16.  If y = -4.8 when x = -1.6, find x when y = -24.  Remember y = kx where k is the constant of variation  The slope is the same as the constant of variation.  Find the direct variation equation and then solve.  If y = 4 when x = 2, find y when x = 16.  If y = -4.8 when x = -1.6, find x when y = -24.

Graphing Direct Variation Equations  Step 1: Graph (0,0)  Step 2: Write the slope as a fraction.  Step 3: Move from (0,0) using the slope as rise/run.  Graph the following:  y = 4x  y = -2/3x  Step 1: Graph (0,0)  Step 2: Write the slope as a fraction.  Step 3: Move from (0,0) using the slope as rise/run.  Graph the following:  y = 4x  y = -2/3x

Inverse Variation  Remember y = k/x  Find the inverse variation equation and then solve.  If y = 4 when x = -3, find y when x = 24.  If y = -2 when x = -7, find x when y = 12.  Remember y = k/x  Find the inverse variation equation and then solve.  If y = 4 when x = -3, find y when x = 24.  If y = -2 when x = -7, find x when y = 12.

Slope-Intercept Form  y = mx + b  m = slope  b = y-intercept  Write in slope-intercept form:  Slope: 8, y-intercept: -3  Slope: -2, y-intercept: -1  y = mx + b  m = slope  b = y-intercept  Write in slope-intercept form:  Slope: 8, y-intercept: -3  Slope: -2, y-intercept: -1

Graphing Equations in Slope-Intercept Form  Step 1: Graph the y-intercept  Step 2: Turn the slope into a fraction  Step 3: Count from the y-intercept using the slope (rise/run)  Step 4: Draw the line  Step 5: Label the line  Graph:  y = -2x - 1  3y = 2x - 6  Step 1: Graph the y-intercept  Step 2: Turn the slope into a fraction  Step 3: Count from the y-intercept using the slope (rise/run)  Step 4: Draw the line  Step 5: Label the line  Graph:  y = -2x - 1  3y = 2x - 6

Write an Equation in Slope-Intercept Form  Given the slope and a point  Step 1: Plug all the information into y=mx+b and solve for b  Step 2: Set up the equation using m and b.  Examples  m = 3, (-2,5)  m = -2/3, (9,-3)  Given the slope and a point  Step 1: Plug all the information into y=mx+b and solve for b  Step 2: Set up the equation using m and b.  Examples  m = 3, (-2,5)  m = -2/3, (9,-3)

 Given 2 points.  Step 1: Find the slope.  Step 2: Plug all the information into y=mx+b and solve for b.  Step 3: Set up the equation using m and b.  Examples:  (-1,6) and (7,-10)  (0,2) and (1,7)  Given 2 points.  Step 1: Find the slope.  Step 2: Plug all the information into y=mx+b and solve for b.  Step 3: Set up the equation using m and b.  Examples:  (-1,6) and (7,-10)  (0,2) and (1,7) Write an Equation in Slope-Intercept Form

 Using a table.  Step 1: Find the slope.  Step 2: Pick off the first ordered pair.  Step 3: Plug all the information into y=mx+b and solve for b  Step 3: Set up the equation using m and b.  Examples.  Using a table.  Step 1: Find the slope.  Step 2: Pick off the first ordered pair.  Step 3: Plug all the information into y=mx+b and solve for b  Step 3: Set up the equation using m and b.  Examples. Write an Equation in Slope-Intercept Form

 Using real world data  JUST LIKE using 2 points! Don’t let the words confuse you!!  The cost for 7 dance lessons is $82, and the cost for 11 lessons is $122. Write a linear equation to find the total cost. Then use the equation to find the cost of 4 lessons.  Using real world data  JUST LIKE using 2 points! Don’t let the words confuse you!!  The cost for 7 dance lessons is $82, and the cost for 11 lessons is $122. Write a linear equation to find the total cost. Then use the equation to find the cost of 4 lessons. Write an Equation in Slope-Intercept Form

Point-Slope Form  y - y 1 = m (x - x 1 )  m = slope  (x 1, y 1 ) = point on the line  Write the equation in point-slope form  (2,1) m = 4  (-7,2) m = 6  y - y 1 = m (x - x 1 )  m = slope  (x 1, y 1 ) = point on the line  Write the equation in point-slope form  (2,1) m = 4  (-7,2) m = 6

Point-Slope Form to Standard Form  Write the equation in standard form  REMEMBER Ax + By = C  Where A,B, and C are integers with no common factor.  y + 2 = -3(x - 1)  y + 4 = -2/5(x - 1)  Write the equation in standard form  REMEMBER Ax + By = C  Where A,B, and C are integers with no common factor.  y + 2 = -3(x - 1)  y + 4 = -2/5(x - 1)

Point-Slope Form to Slope-Intercept Form  Write the equation in slope-intercept form:  y=mx+b  y + 4 = 4(x - 2)  y - 8 = -1/4(x + 8)  Write the equation in slope-intercept form:  y=mx+b  y + 4 = 4(x - 2)  y - 8 = -1/4(x + 8)

Writing an Equation in Point- Slope Form using 2 Points  Step 1: Find the slope.  Step 2: Pick a point.  Step 3: Set up the equation  (-4,2) and (8,1)  (10,-5) and (2,8)  Step 1: Find the slope.  Step 2: Pick a point.  Step 3: Set up the equation  (-4,2) and (8,1)  (10,-5) and (2,8)

Equations of Vertical Lines  The equation is of the form x = a  Write the equation  (12,-3) and (12,10)  (apple, 500) and (apple, 230)  The equation is of the form x = a  Write the equation  (12,-3) and (12,10)  (apple, 500) and (apple, 230)

Parallel and Perpendicular Lines  Determine whether the lines are parallel or perpendicular  Examples  2y = 3x + 6 4y - 6x = 20  y = 2x - 5x + 3 3y = x +10  Determine whether the lines are parallel or perpendicular  Examples  2y = 3x + 6 4y - 6x = 20  y = 2x - 5x + 3 3y = x +10

Parallel Lines  Find the equation of the line that passes through the point and is parallel to the line.  (-2,2), y = 4x - 2  (4,-6), x + 2y = 5  Find the equation of the line that passes through the point and is parallel to the line.  (-2,2), y = 4x - 2  (4,-6), x + 2y = 5

Perpendicular Lines  Find the equation of the line that passes through the point and is perpendicular to the line.  (6,-2), y = -3x - 6  (-1,3), 2x + 4y = 12  Find the equation of the line that passes through the point and is perpendicular to the line.  (6,-2), y = -3x - 6  (-1,3), 2x + 4y = 12

STUDY!!!  This is A LOT of information!!  You have to study your notes and homework to make sure you can do all of the problems!  There will be no surprises!  This is A LOT of information!!  You have to study your notes and homework to make sure you can do all of the problems!  There will be no surprises!