Linear Functions

Length of a Side of a Square Yard Compare and Contrast Yards to Feet Number of Feet Number of Yards Yards to Square Yards Length of a Side of a Square Yard Area of Square (yd2)

Tables: Linear or Nonlinear Is the rate of change constant (the same)? x y 2 50 4 35 6 20 8 5 x y 1 4 16 7 49 10 100 +3 +15 +2 -15 +2 -15 +3 +33 +2 +3 +51 -15 linear nonlinear

Identify: Linear or Nonlinear Table? x y 20 5 16 10 12 15 8 x 2 4 6 y 8 18 nonlinear linear

Graphs: Linear or Nonlinear Is the graph a straight line? linear nonlinear linear

Identify: Linear or Nonlinear Graph?

Equations: Linear or Nonlinear REMEMBER: x1 = x and x0 = 1 In “y = ” form, is x raised to a power of 1 or 0? Does x appear in the numerator? y = 6/x y = x3 + 1 y = x + 4 nonlinear y = ½ x nonlinear y = 4 linear linear linear

Identify:Linear or Nonlinear Equation? 3x 2 y = .6x1 y = x2 + 8 y = 2/x + 5 linear nonlinear linear nonlinear

Pointers to Keep in Mind A table is linear if the rate of change is constant. There is a common difference. A graph is linear if it is a straight line. An equation is linear if the power of x is either 1 or 0 and it appears in the numerator.

Exit Slip Identify if linear or nonlinear. Table A Equation y = + 5 3 6 9 12 y 10 8 y = + 5 8 x Graph a b c

Review of Formulas Formula for Slope Standard Form *where A>0 and A, B, C are integers Slope-intercept Form Point-Slope Form

Change into standard form.

x-intercepts and y-intercepts The intercept is the point(s) where the graph crosses the axis. To find an intercept, set the other variable equal to zero.

Graphing Lines graph a line. Using x and y intercepts: *You need at least 2 points to graph a line. Using x and y intercepts: Find the x and y intercepts Plot the points Draw your line

Graph using x and y intercepts 2x – 3y = -12 x-intercept 2x = -12 x = -6 (-6, 0) y-intercept -3y = -12 y = 4 (0, 4)

Graph using x and y intercepts 6x + 9y = 18 x-intercept 6x = 18 x = 3 (3, 0) y-intercept 9y = 18 y = 2 (0, 2)

Vertical Lines Slope is undefined. Equation form is x = #. Write an equation of a line and graph it with undefined slope and passes through (1, 0). x = 1 Write an equation of a line that passes through (3, 5) and (3, -2). x = 3

Horizontal Lines Slope is zero. Equation form is y = #. Write an equation of a line and graph it with zero slope and y-intercept of -2. y = -2 Write an equation of a line and graph it that passes through (2, 4) and (-3, 4). y = 4

Review of Formulas Formula for Slope Standard Form *where A>0 and A, B, C are integers Slope-intercept Form Point-Slope Form

Change into slope-intercept form and identify the slope and y-intercept.

Write an equation for the line that passes through (-2, 5) and (1, 7): Find the slope: Use point-slope form:

Graphing Lines Using slope-intercept form y = mx + b: Change the equation to y = mx + b. Plot the y-intercept. Use the numerator of the slope to count the corresponding number of spaces up/down. Use the denominator of the slope to count the corresponding number of spaces left/right. Draw your line.

Graph using slope-intercept form y = -4x + 1: y-intercept (0, 1) Slope m = -4 = -4 1

Graph using slope-intercept form 3x - 4y = 8 y = 3x - 2 4 y-intercept (0, -2) Slope m = 3 4