$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 Linear Functions Slope Parallel & Perpendicular Lines Different Forms of Linear Equations Solving for y Misc. Linear Functions

Explain how you know if a graph represents the following: Function: Linear function: Direct Variation: $100 Question Linear Functions

$100 Answer Linear Functions Function: passes VLT Linear function: passes VLT & straight line Direct Variation: passes VLT, straight line & crosses through (0,0)

$200 Question Linear Functions Which table(s) are linear? Explain how you know. A. B.

$200 Answer Linear Functions B.) x and y are both going up with constant rates * same rate of change * Rate of change = change of y change of x Table A – not a constant rate of change

$300 Question Linear Functions Which of the following equations is not linear? Explain or show how you know. A)y = 2x 2 – 7 B) -6 = y C) 4x – 2y = 10 D) y = 3x + 1

$300 Answer Linear Functions A)y = 2x 2 – 7not linear--exponent B) -6 = y horizontal—straight line C) 4x – 2y = 10 standard form x and y-int. --line D) y = 3x + 1 slope-int.—always form a line

$400 Question Linear Functions Explain if each equation represents a direct variation (proportional relationship). Identify the constant of variation if it is a direct variation. A.) 3y = 4x + 1B.) y + 3x = 0

$400 Answer Linear Functions Solve each equation for y. Look to see if it’s in y = kx formk = constant of variation A.) 3y = 4x + 1 y = 4/3x + 1 Not in y = kx form (+1) B.) y + 3x = 0 y = -3x Yes, in y = kx form k = m -3

$500 Question Linear Functions Let y = 2x + 9. If the value of x increases by 6, which of the following best describes the change in the value of y. a.) decreases by 6 b.) increases by 6 c.) increases by 12 d.) increases by 21

$500 Answer Linear Functions As x goes up by 6 The value of y. c.) increases by 12

$100 Question Slope Find the slope of the line (0, 4) (3, -5)

$100 Answer Slope Rise m = -3 Run

$200 Question Slope Write the equation of the line that passes through each pair of points in slope- intercept form (6, 5) and (1, 2)

$200 Answer Slope 1. Label Points 2. Use slope formula 3.Remember neg. divided by a neg. is positive 4. Equation: y – 2 = 3/5(x – 1) or y - 5 = 3/5(x – 6) or y = (3/5)x + 1.4

$300 Question Slope Put the following equation into slope- intercept form. Identify the slope and y- intercept. Then use the slope and y-int. to graph the line. 3x – y = 2

$300 Answer Slope 3x – y = 2y = 3x -2 m = 3 -3x -3x b = -2 -y = -3x

$400 Question Slope Laurel graphed the equation y = -2x + 5. Katelyn then graphed an equation that was a line that was not as steep as Laurel’s. Which equation could have been the one Katelyn graphed? a.) y = -3x + 5b.) y = 1/2x + 6 c.) y = 4x – 2 d.) y = -2x + 3

$400 Answer Slope B.) y = 1/2x + 6 is not as steep. Fractions (between -1 and 1: non-improper) are less steep than any integer— even if it’s negative.

$500 Question Slope The cost of hiring Zach as a painter is given by the linear equation C = 10h + 100, where h is the number of hours Zach works. Identify the slope and y-int. What does the slope of the line represent? What does the y-intercept represent?

$500 Answer Slope m = 10 The slope means Zach earns $10 per hour. b = 100 The y-intercept represents base charge of hiring Zach

$100 Question Parallel & Perpendicular Lines What are two different ways that lines can be perpendicular?

$100 Answer Parallel & Perpendicular Lines Vertical lines are perpendicular to a horizontal lines. Ex. x = 3 and y = -2 When the product of slopes = -1 Ex. 4 and -1/4

$200 Question Parallel & Perpendicular Lines A line has the equation x + 2y = 5 What is the slope of a line parallel to this line? a.) – 2b.) - ½ c.) ½d.) 2

$200 Answer Parallel & Perpendicular Lines A line has the equation x + 2y = 5 1.Put line in slope-int. form y = -1x Parallel -- same slope -- b.) - ½

$300 Question Parallel & Perpendicular Lines

A. 1 and -1 are “opposite reciprocals” $300 Answer Parallel & Perpendicular Lines

$400 Question Parallel & Perpendicular Lines

$400 Answer Parallel & Perpendicular Lines Line AB has a slope of 1 and Line BC has a slope of -3/2 and Line AC has a slope of 0. None of the slopes will have a product of -1 so D is the answer

$500 Question Parallel & Perpendicular Lines Write an equation that is perpendicular to the given line below that passes through the point (- 6, 2)

$500 Answer Parallel & Perpendicular Lines 1.Slope will be -3 (opp. reciprocal) 2.Use point-slope form y- 2 = -3(x – (-6)) Distributive Prop. y = -3x -16

$100 Question Different Forms of Linear Equations Find and use the x and y intercepts to graph the line. -x + 3y = 6

$100 Answer Different Forms of Linear Equations -x + 3y = y = 6-x + 3(0) = 6 y-int. = 2 -x = 6 (0,2) x-int. = -6 (-6,0) (0,2)

$200 Question Different Forms of Linear Equations Find and use the x and y intercepts to graph the line. -2x = y

$200 Answer Different Forms of Linear Equations -2x = y -4y from both sides -2x - 4y = 12 Now in standard form x-int. = (-6,0) y-int. = (0,-3) (-6,0) (0, -3)

$300 Question Different Forms of Linear Equations What is the x-intercept of the linear function f(x) = -3x + 6? Note: f(x) is dependent variable (y) a.) -2b.) 2c.) 3 d.) 6

$300 Answer Different Forms of Linear Equations f(x) = -3x + 6 Think: y = -3x + 6 add 3x to both sides –standard form y + 3x = x = 6 x-int. = 2 (b)

$400 Question Different Forms of Linear Equations A line has a slope of and passes through the point (-3, 4). What is the equation of the line in point-slope form? What is the equation of the line in slope-intercept form?

$400 Answer Different Forms of Linear Equations Point-slope form y- 4 = [x – (-3)] y – 4 = (x + 3) Slope-Intercept Form y = x + 6

$500 Question Different Forms of Linear Equations Is every linear relationship a direct variation? Is every direct variation a linear relationship? Explain.

$500 Answer Different Forms of Linear Equations Every linear relationship is not a direct variation—only if the y-int. is 0. However, every direct variation is linear because it has a constant rate of change. Direct Variation: y = 3x (also linear) Not a direct variation y = 3x +5 (is linear)

$100 Question Solving for y Solve the equation for y: x + y = 4

$100 Answer Solving for y y = -x + 4

$200 Question Solving for y: Solve for y: -2x + 4y = 8

$200 Answer Solving for y -2x + 4y = 8 + 2x 4y = 2x y = 0.5x + 2

$300 Question Solving for y Solve for ya and then state the slope and the y-intercept: 4x – y = 6

$300 Answer Solving for y 4x – y = 6 - 4x - 4x -y = -4x y = 4x – 6 Slope = 4; y-intercept = -6

$400 Question Solving for y Solve for y and then give the slope of a line that would be perpendicular to that line: 3x + 4y = 8

$400 Answer Solving for y 3x + 4y = 8 -3x 4y = -3x The slope of this line is -3/4, so a line perp. to this would have slope of 4/3

$500 Question Solving for y Write an equation of a line that would be perpendicular to this line and also go through the point (-3,4): 2x – 6y = 8

$500 Answer Solving for y Slope of this line is: 2x – 6y = 8 -2x -2x -6y = -2x y = 1/3x – 1.3, slope is 1/3, so the perpendicular slope would be -3. The line must also go through (-3,4): y – 4 = -3(x + 3) or y = -3x -5

$100 Question Miscellaneous The table shows an employee’s pay per hour. Determine if there is a direction variation between the pay and number of hours worked. If so, find the equation of direct variation

$100 Answer Miscellaneous You can use the ratio to check. 17/2 = 8.5 and 34/4 = 8.5 ratios are = (proportional) so it’s a direct variation The equation would be y = 8.5x

$200 Question Miscellaneous Describe the transformation from f(x) to g(x): f(x) = 4x – 2, g(x) = 1/2x + 3

$200 Answer Miscellaneous f(x) = 4x – 2, g(x) = 1/2x + 3 From f(x) to g(x), the graph is rotated about (0,0) (g(x) is less steep), and is then translated 5 units up.

$300 Question Miscellaneous Write the equation of the line that passes through each pair of points in slope- intercept form (-1, 5) and (2, -4)

$300 Answer Miscellaneous 2. ) Choose a point (-1,5) Insert into slope-int. and solve for b OR Use point-slope form then solve for y Y = -3x ) Find Slope m = -3

$400 Question Miscellaneous Also, explain what each intercept represents

$400 Answer Miscellaneous x-intercept (8,0) Namia has enough money to buy 8 lg. popcorns and 0 drinks 4-intercept (0,20) Namia has enough money to buy 20 small drinks and 0 popcorns

$500 Question Miscellaneous Prove that ABCD is a parallelogram

$500 Answer Miscellaneous ABCD is a parallelogram because opposite sides are parallel. Line AB and Line DC both have a slope of -2/3 and Line AC and Line DC both have an undefined slope (vertical lines), so there are two sets of parallel sides.

Write an equation in slope-intercept form for the given table. Explain what the slope and y-intercept form represent. Then find the cost for 60 additional minutes. Final Jeopardy

Find the rate of change for slope m = 2/5 or 0.4 (0.40 for each add. min.) Pick a point and use slope formula or solve for b to get slope intercept form y = 0.4x + 40 y –int. means it cost $40 with 0 add. min. y = 0.4(60) + 40 It will cost $64 for 60 additional minutes.