Algebra II
Chapter 2
2.2 Linear Equations

Objective/ Big Idea
Write or identify a linear equation in standard form
 Find the slope of an equation in standard form
Introductory Problem:
Tony has a meal plan as part of his college dorm package. Breakfast is $3.50 and lunch and
dinner cost the same at $5.00 per meal. His meal plan allows him to spend $70 per week.
An equation that represents this is:
and y is the number of lunch and dinner combined.
where x is the number of breakfasts
This equation is written in standard form. Standard form is Ax + By = C Some
authors require that A, B, and C be integers, but that isn’t always practical
when one is dealing with applied problems. Standard form does have to have x
and y on one side of the equation and a constant be on the other side. It is
most often used in situation where a constant amount is split between two
options with different rates.
a.
What is the y-intercept of Tony’s equation above? (0, _________) What does the
intercept mean in the context of the problem?
y
b. What is the x-intercept of Tony’s equation
above? (_________, 0) What does the
intercept mean in the context of the
problem above?
c. Since we can graph an equation once we have two
points, plot the two intercepts and then connect
them with a straight line. Then, find the slope
based off the graph. Interpret the slope based on
the problem context.
d. We also spent time talking about slope-intercept form. Rearrange the equation:
for y. How might you graph the equation using this information?
x
The introductory problem, introduced two different ways to graph a standard form
equation. Find the x and y intercepts and graph, or rearrange the equation into
slope-intercept form and graph.
Example:
3x – 5y = 30
Method 1
Find and graph the x and y intercepts
Method 2
Rearrange the equation to slope intercept
form and then graph.
Teamwork:
1. Examine the following linear equations written in standard form. For each
equation, determine the x-intercept and the y-intercept. (Remember: the xintercept can be found by replacing y with 0 to obtain the point (
, 0); the yintercept can be found by replacing x with 0 to obtain the point (0, ).
a. 2x + 5y = 10
b. 3x + 4y = 12
c. 4x – 3y = 24
d. 6x – 5y = 30
e. - 2x + 4y = 12
f. x – 10y = 10
2. Graph each of the equations found in #1 by sketching the line through the xintercept and y-intercept. Put 3 equations on each grid.
3. For each of the graphs/equations in part 1, find the slope from the graph.
Record them below.
a.
b.
c.
d.
e.
f.
4. Rewrite each of the equations in slope-intercept form. Then identify the slope
of each line.
a.
c.
e.
2x + 5y = 10
4x – 3y = 24
- 2x + 4y = 12
b. 3x + 4y = 12
d. 6x – 5y = 30
f.
x – 10y = 10
5. Is the slope determined by the graph, the same as the slope given by re-writing
the equation in slope-intercept form?
6. Explain how it would be possible to determine the slope of the line from the
standard form of the equation. Be specific in explaining your method(s).
7. Solve the equation Ax + By = C for y.
8. Compare your results in #7 with your explanation in #6.
Assignment: page 67 – 68: 9 – 10, 32 – 37, 69