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 EquationsGraphing Linear Inequalities and SystemsMisc. Linear Functions$300 Question Graphing Linear Inequalities and Systems of EquationsSolve the system by graphing2y = 83y = 2x + 6SlopeParallel & PerpendicularLines

Different Forms Of Linear EquationsGraphing Linear InequalitiesSystems of EquationsMiscellaneous $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 (-1, 5) and (2, -4)$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 = 10t + 100,where t 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 another way to write ya.) -2b.) 2c.) 3 d.) 6$400 Question Different Forms of Linear EquationsA line has a slope of 2/3 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 Graphing Linear Inequalities and Systems of EquationsGraph each inequalityy > -3x + 2$200 Question Graphing Linear Inequalities and Systems of EquationsGraph each inequality4x + y 1DailyDouble!!click box when ready

$400 Question Graphing Linear Inequalities and Systems of EquationsSolve the system by graphingy 1 = 2x-y = -2x -1$500 Question Graphing Linear Inequalities and Systems of Equations

$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 MiscellaneousSolve the system by substitutionx = 2y + 6y = -3x + 4 $300 Question MiscellaneousSolve the system of equationsx y = 4x 2y = 10$400 Question Miscellaneous

$500 Question Miscellaneous

Solve the system of equations by elimination

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 (are negative reciprocals) 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 = 2/3[x (-3)]y 4 = 2/3(x + 3)Slope-Intercept Form y = 2/3x + 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 Graphing Linear Inequalities and Systems of Equationsm = -3 b = 2Dashed(0,0) not a solution

$200 Answer Graphing Linear Inequalities and Systems of EquationsSolve for ym = -4 b = 1Solid Line(0,0) is a solution

$300 Answer Graphing Linear Inequalities and Systems of Equations

$400 Answer Graphing Linear Inequalities and Systems of Equations

$500 Answer Graphing Linear Inequalities and Systems of Equations

Find x and y-intercepts to graphSolid Line(0,0) is a solution$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

Could have also substituted top equation into the bottom. $300 Answer Miscellaneous

Could have used other ways to eliminate or you could have used the substitution or graphing methodsRemember to check your answer by substituting solution into each original equation. $400 Answer Miscellaneous

$500 Answer Miscellaneous

Could have also eliminated the ysRemember to check your answer by substituting solution into each original equation. FinalJeopardy