Linear Equations in Two Variables

1
Linear Equations in Two Variables

• 2.2
• SSC 105

2
Linear Equations in Two Variables
Let A, B, and C be real numbers such that A and B
are not both zero. A linear equation in two
variables is an equation that can be written in
the form Ax By C This form is called
standard form.
3
Determining Solutions
4
GRAPHING
5
GRAPHING
6
The X- and Y- Intercets
An x-intercept of an equation is a point (a, 0)
where the graph intersects the x-axis. A
y-intercept of an equation is a point (0, b)
where the graph intersects the y-axis.
STEPS TO FIND THE INTERCEPTS Given an equation
in x and y, 1. Find the x-intercept(s) by
substituting y 0 into the equation and solving
for x. 2. Find the y-intercept(s) by substituting
x 0 into the equation and solving for y.
7
A picture
8
Find the intercepts and graph.
9
Interpreting X and Y intercepts

• Acme motor company tests the engines of its
  trucks by running the engines in a laboratory.
  The engines burn 4 gal of fuel per hour. The
  engines begin the test with 30 gal of fuel. The
  equation y 30 4x represents the amount of
  fuel y left in the engine after x hr.
• Find the x- and y-intercepts.
• Interpret the y-intercept in the context of this
  problem.
• Interpret the x-intercept in the context of this
  problem.

10
Answers

• X-int (7.5, 0) Y-int (0, 30)
• The y-intercept means that initially (at 0 hrs)
  there is 30 gal of fuel in the truck.
• The x-intercept means that after 7.5 hrs., there
  is 0 gal of fuel. The truck is empty.

11
Horizontal Lines
Horizontal Lines are always in the form Y a
They have no x intercept
It crosses the y axis at 3! So, y intercept is
(0, 3)
12
Vertical Lines
Vertical Lines are always in the form x a
They have no y intercept
It crosses the x axis at 2! So, x intercept is
(2, 0)