1. Do Now

2. 2.3 Linear Functions and Slope-Intercept Form
Learning Target:
I can
Graph linear equations
I can write equations of lines.

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

4. Review Slope

5. Examples of linear equations
Equation is in Ax + By =C form
Rewrite with both variables on left side …
x + 6y =3
B =0 … x + 0 y =1
Multiply both sides of the equation by -1 … 2a – b = -5
Multiply both sides of the equation by 3 … 4x –y =-21
2x + 4y =8
6y = 3 – x
x = 1
-2a + b = 5

6. Examples of Nonlinear Equations
The following equations are NOT in the standard form of Ax + By =C:
The exponent is 2
There is a radical in the equation
Variables are multiplied
Variables are divided
4x2 + y = 5
xy + x = 5
s/r + r = 3

7. Find the slope of a line through points (3, 4) and (-1, 6).

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

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

10. Change into standard form.

11. 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.

12. 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

13. 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

14. 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

15. 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)

16. 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)

17. 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.

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

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

20. Homework
Homework: p. 78 #7, 11, 17, 19, 23, 25, 27, 29, 31, 33, 37, 39, 43, 49, 53 Challenge - # 62