Linear Functions

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 (yd 2 )

Tables: Linear or Nonlinear linear nonlinear xy xy  Is the rate of change constant (the same)?

Identify: Linear or Nonlinear Table? linear xy x0246 y02818  nonlinear

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

Identify: Linear or Nonlinear Graph?  linear  nonlinear

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

Identify:Linear or Nonlinear Equation? y = 2/x + 5y = x 2 + 8y =.6x 1 y = + 1 3x 2 linear nonlinear

Pointers to Keep in Mind A graph is linear if it is a straight line.  A table is linear if the rate of change is constant. There is a common difference.  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. 1.Table A 2.Graph 3.Equation x36912 y 1086 abc y = x

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

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 * 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 Slope-intercept Form Point-Slope Form *where A>0 and A, B, C are integers

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: Slope m = -4 = -4 1 y-intercept (0, 1)

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