3. Linear Functions

4. 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)

5. 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

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

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

8. Identify: Linear or Nonlinear Graph?

9. 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

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

11. 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.

12. Exit Slip Identify if linear or nonlinear. Table A Equation y = + 53 6 9 12 y 10 8
y = 8 x
Graph a b c

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

14. Change into standard form.

15. 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.

16. 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

17. 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)

18. 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)

19. 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

20. 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

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

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

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

24. 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.

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

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