Linear Functions

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$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$500Linear FunctionsSlopeParallel & PerpendicularLinesDifferent Forms of Linear EquationsSolving for yMisc. Linear Functions$300 Question Solving for y

Solve for ya and then state the slope and the y-intercept:

4x y = 6

SlopeParallel & PerpendicularLines

Different Forms Of Linear EquationsSolving for yMiscellaneous $100 Question Slope

Find the slope of the line(0, 4)(3, -5)$200 Question SlopeWrite the equation of the line that passes through each pair of points in slope-intercept form (6, 5) and (1, 2)$300 Question SlopePut 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 $400 Question SlopeLaurel graphed the equation y = -2x + 5. Katelyn then graphed an equation that was a line that was not as steep as Laurels. Which equation could have been the one Katelyn graphed?a.) y = -3x + 5b.) y = 1/2x + 6c.) y = 4x 2 d.) y = -2x + 3

$500 Question SlopeThe 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?

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

$200 Question Parallel & Perpendicular LinesA line has the equation x + 2y = 5

What is the slope of a line parallel to this line?a.) 2b.) - c.) d.) 2

$300 Question Parallel & Perpendicular Lines

$400 Question Parallel & Perpendicular Lines

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

$100 Question Different Forms of Linear EquationsFind and use the x and y intercepts to graph the line.-x + 3y = 6$200 Question Different Forms of Linear EquationsFind and use the x and y intercepts to graph the line.-2x = 12 + 4y$300 Question Different Forms of Linear EquationsWhat 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$400 Question Different Forms of Linear EquationsA 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?

$500 Question Different Forms of Linear EquationsIs every linear relationship a direct variation? Is every direct variation a linear relationship? Explain.$100 Question Solving for ySolve the equation for y:x + y = 4$200 Question Solving for y:Solve for y:-2x + 4y = 8DailyDouble!!click box when ready

$400 Question Solving for ySolve for y and then give the slope of a line that would be perpendicular to that line: 3x + 4y = 8$500 Question Solving for yWrite an equation of a line that would be perpendicular to this line and also go through the point (-3,4): 2x 6y = 8$100 Question Miscellaneous

The table shows an employees 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$200 Question MiscellaneousDescribe the transformation from f(x) to g(x): f(x) = 4x 2 , g(x) = 1/2x + 3$300 Question MiscellaneousWrite the equation of the line that passes through each pair of points in slope-intercept form (-1, 5) and (2, -4)$400 Question Miscellaneous

Also, explain what each intercept represents$500 Question Miscellaneous

Prove that ABCD is a parallelogram

A. 1 and -1 are opposite reciprocals$300 Answer Parallel & Perpendicular Lines$400 Answer Parallel & Perpendicular LinesLine 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 Answer Parallel & Perpendicular LinesSlope will be -3 (opp. reciprocal)Use point-slope form y- 2 = -3(x (-6)) Distributive Prop. y = -3x -16$100 Answer Different Forms of Linear Equations-x + 3y = 6-x + 3y = 60 + 3y = 6-x + 3(0) = 6y-int. = 2 -x = 6(0,2) x-int. = -6 (-6,0)

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

(-6,0)(0, -3)$300 Answer Different Forms of Linear Equationsf(x) = -3x + 6 Think: y = -3x + 6add 3x to both sides standard formy + 3x = 60 + 3x = 6 x-int. = 2 (b)$400 Answer Different Forms of Linear EquationsPoint-slope form y- 4 = [x (-3)]y 4 = (x + 3)Slope-Intercept Form y = x + 6

$500 Answer Different Forms of Linear EquationsEvery linear relationship is not a direct variationonly 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 Answer Solving for y

y = -x + 4

$200 Answer Solving for y

-2x + 4y = 8+ 2x + 2x 4y = 2x +8 4 4 y = 0.5x + 2$300 Answer Solving for y 4x y = 6 - 4x - 4x -y = -4x + 6 -1 -1 y = 4x 6Slope = 4; y-intercept = -6$400 Answer Solving for y3x + 4y = 8-3x -3x 4y = -3x + 8 4 4The slope of this line is -3/4, so a line perp. to this would have slope of 4/3$500 Answer Solving for ySlope of this line is: 2x 6y = 8 -2x -2x -6y = -2x + 8 -6 -6 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 Answer MiscellaneousYou can use the ratio to check.

17/2 = 8.5 and 34/4 = 8.5 ratios are = (proportional) so its a direct variationThe equation would be y = 8.5x

$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 Answer Miscellaneous

2. ) Choose a point (-1,5)Insert into slope-int. and solve for b ORUse point-slope form then solve for y

Y = -3x + 2 1.) Find Slope m = -3$400 Answer Miscellaneous

x-intercept (8,0)Namia has enoughmoney to buy 8 lg.popcorns and 0 drinks4-intercept (0,20)Namia has enoughmoney to buy 20 small drinks and 0 popcorns$500 Answer MiscellaneousABCD is a parallelogram because opposite sidesare parallel.

Line AB and Line DC both have a slope of -2/3and 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 slopem = 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 formy = 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.