1. Lesson 2-2
Linear Equations

2. Linear function – a function whose graph is a line.
A linear function is represented by a linear equation.
ex) y = 2x + 3
A solution of a linear equation is an ordered pair.

3. y = 3x + 2 Because the value of y depends on the value of x, y is called the DEPENDENT VARIABLE and x is called the INDEPENDENT VARIABLE

4. When graphing a linear equation make a t-chart.
y = 3x + 2
To be sure you didn’t make a mistake graph at least three points.

5. y-intercept – point where the line crosses the y axis.
What is the value of x at the y-intercept.
x-intercept – point where the line crosses the x axis.
What is the value of y at the x-intercept.

6. Slope
Slope = vertical change = rise = y2 – y1 horizontal change run x2 – x1 Find the slope of the line that goes through the points ( -2, -2) and (4, 2)

7. Standard Form of a linear equation – is in the form
Ax + By = C
A must be positive.
A, B, and C are integers.
You can graph a linear equation in Standard Form by using the intercepts

8. When an equation is in standard form the slope = -A/B
2x + 3y = 7

9. Slope-intercept form
y = mx + b
slope y-intercept

10. Graph from Slope intercept form
Put the y-intercept on the graph and use the slope to find other points

11. Write in standard form an equation of a line with slope 2 through (4, -2)

12. If you are given two points and asked to write an equation, Find the slope first, then write the equation.
(5,0) (-3, 2)

13. Point-Slope Form
The line through point (x1, y1) with slope m has the equation:
y – y1 = m(x – x1)

14. Standard Form: Ax + By = C
Point Slope Form: y – y1 = m(x – x1)
Slope Intercept: y = mx + b

15. Horizontal lines
m = 0
y is constant

16. Vertical Lines
m is undefined
x is constant

17. Parallel Lines
m = m
b1 = b2

18. Perpendicular Lines
m2 is the opposite reciprocal of m1
m1 = -1/ m2

19. 2-64 even pg