Algebra 2/Trig Name: ____________________________________
Goals

Identify a linear equation. Graph a linear equation from a given equation and from a table of values. Find the slope of a line and write a linear equation (in standard and slope intercept form) from a graph, a set of points, or a table. Graph an equation in standard form.
Example 1: Represent a real-world linear relationship in a table, graph or equation
A tax accountant charges a fixed fee of $300 for an initial meeting and $175 per hour for all hours worked after the initial meeting. a. Make a table of the total charges for 1, 2, 3, and 4 hours worked.
Hours worked (w)
Total Charge (c)
1 2 3 4 b. Graph the points represented by your table and connect them. c. Write a linear equation to model this situation. What variables should we use? Which is the independent
variable? Which is the dependent variable? d. How much will you be charged for 30 hours of work?
Linear equations that model situations typically have common characteristics. They follow the form: total amount = variable amount + fixed amount
Example 2: Graph a Linear Equation
Graph: 𝑦 =
3
5 𝑥 + 2 using a table of values.
How else could we graph the equation?

Example 3: Slope-Intercept Form
Slope-intercept form is: ____________________________________________ m represents the _________________________________ and b represents the ______________________.
1
Graph: 𝑦 =
2 𝑥 − 1 using the slope and y-intercept.
Example 4: Tables of values and linear relationships
A table of values represents a linear relationship when there is a _______________ difference in the x-values and a
_________________ difference in the y-values.
Which of the following tables represent a linear relationship? a. x 2 4 6 8 y 3 7 10 14 b. x y
-2
-4
Example 5: Slope of a line
RECALL - Formula for slope:
0
2
2
8
4
14
Given 2 points, (-2, 7) and (4, 6) find the slope of a line.

Example 6: Slope intercept form given two points
Given the points (1, -3) and (3, -5) lie on the same line, find the equation of the line that passes through the two of them in slope-intercept form.
1. Find the slope
2. Substitute the slope and one of the points into y = mx + b , and solve for b .
3. Use the slope and y-intercept to write your equation.
Example 7: Standard Form
The standard form of a linear equation is ________________________________, where A, B and C are real integers and A and B are not both 0. A should be_______________. a. Use intercepts to graph the equation 5x – 2y = 10. b. Horizontal lines: Find the slope of the horizontal line that contains the points (-4, 4) and (5, 4).
A horizontal line is a line that has a slope of _____________. c. Vertical lines: Find the slope of the vertical line that contains the points (3, 5) and (3, -9).
A vertical line is a line that has an ___________________________________________. Why?

Checkpoints:
1. Given the points (-4, 5) and (6, -3) lie on the same line, find the equation of the line.
2. Given a table of values, graph the points and write the equation of the line. x -6 -3 0 3 y 2 3 4 5
3. Use the x and y intercepts to graph 3 x – 6 y = 18.
4. Sketch a graph of the following equations: x = 6
Homework: p. 8 – 10 Problems 9 – 36 (3rds), 49 – 54 All AND p. 17 – 18 Problems 12 – 63 (3rds) and 64 & 65
You will need graph paper, available on side counter. y = -4