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MAT 1033 - Review Section 3 Graphing Linear Functions A linear function is a function with no exponents, no variables in the denominator, and no special symbols. To "solve" a LINEAR FUNCTION, make a graph. The line represents the solution. Linear functions can be graphed using any of the following techniques. A. Make a chart and determine at least two ordered pairs. Then plot the points and connect. 1.) y = 5x – 3 2) y = 2 x−3 3 B. When a linear equation is in Standard Form Ax + By = C it is helpful to graph using the x and y intercepts. To find the x-intercept substitute 0 for y. To find the y-intercept substitute 0 for x. Determine the x and y intercepts of the following linear equations and graph the solution. Ex 1: 2x - 3y = 12 Ex 2: 5x + 2y = 8 x-intercept: x-intercept: y-intercept: y-intercept: C. When a linear equation is in the Slope-intercept Form - y = mx + b – it is useful to graph using the y-intercept as your first point and the slope (rise over run) to determine additional point(s). Identify the slope and y-intercept for each function and then graph. 1 x-2 2 Ex 2. y = -3x + 4 Ex 3. y = -x - 1 Slope: Slope: Slope: y-intercpet: y-intercept: y-intercept: Ex 1. y = D. When a linear equation is in any other form, it is often useful to solve the equation for y, then graph using the slope and y-intercept. Solve the following equations for y, identify the slope and y-intercept, then graph the solution. Ex 1. 3y = 4x + 12 Solve for y: Ex 2. 8 + 2y = 6x Slope: y-intercpet: Slope: y-intercept: Ex 3. 5x – 2y = 10 Slope: y-intercept: (Note: You would then graph these equations as those in section C.) E. Review of vocabulary: 1. The slope can be described as _____________. 2. The slope-intercept form of the equation of a line is where _____ is the slope, and _____ is the y-intercept. 3. The standard form of the equation of a line is: ________________. 4. To find the x-intercept substitute ____ for ____ and solve. 5. To find the y-intercept substitute ____ for ____ and solve. F. Review of "methods" for solving: 1. Linear equation: Method: 3(x – 1) + 2 = 5x – 6 2. Polynomial (quadratic) equation: Method: 3. Rational equation: x2 – 7x = 8 1 3 7 − = x 5 2 Method: 4. Linear function: Method: 3x – 8 = 2y HW: Section R3 Page 943 – Problems 13-16,21-24 Hint: When asked for the slope and/or y-intercept, solve for y first. Section 3.3 Page 159 – Problems 17 – 24 all Review HW: Pg 406 Problems 9, 10, 13, 23 (022)