Transcript Linear Equations: How to Graph and Solve

Linear Equations
By:
Emily Zhou
What is a Linear Equation?
• A linear equation is an
equation whose graph
forms a straight line.
• Linear equations are
usually shown on a
coordinate plane
• Real life situations of
linear equations
include the stock
market as well as the
payments of a car.
Parts of a Coordinate Plane
QUADRANT II
QUADRANT I
(-x, y)
(x, y)
Origin
QUADRANT III
(-x, -y)
QUADRANT IV
(x, -y)
Y-Axis
X-Axis
Slope
• Slope is the ratio of vertical change to the
horizontal change (rise/run) of a line.
• Slope in a linear equation shows if the line is
ascending (positive) or descending
(negative).
• Slope can also show the rate of change.
• The letter m is used to represent slope in a
formula.
Forms of Linear Equations
•
•
The forms of linear equations are the formats
in which the information is written in.
These two forms are the most commonly used
ways to write linear equations.
1. Slope Intercept Form: y=mx+b
2. Standard Form: Ax + By =C
Slope Intercept Form
• Slope intercept form is y=mx+b.
• This form makes it easy to find the slope (m) and
the y-intercept (b).
• Working with this form is simple, so it is used
more often than other forms.
Example: y= ¾x + 3
* ¾ is the slope.
* 3 is the point where the line crosses the Y-axis.
Graph Using Slope Intercept Form
I will use the equation
y= ½ x-1 to demonstrate how
to graph a linear equation
using slope intercept form.
1.) First, graph the y-intercept (b).
In this equation, b= -1, so place
a dot on the point (0,-1).
2.) Next, use the slope (½ ) to rise
up once and run twice
horizontally. Plot the point.
3.) Plot as many points as desired
using the slope, then draw a line
through the points.
Run 2
Rise 1
Standard Form
•
•
Standard form for linear equations is
Ax + By=C.
It can be used to find two points on
the line of the equation.
Example: 2x+2y=4
1.) Substitute in a zero for x. Simplify.
2(0)+2y=4
y=2
2.) One point of the line is (0,2). Plot the point.
3.) Substitute y with zero. Simplify.
2x+2(0)=4
x=2
4.) The second point is (2,0). Plot it and draw
a line through the two points.
Using Linear Equations
• Linear equations are not only a main part of
algebra courses, but it is just as important in the
real world.
• If you deposited $40 in the bank every year, and
you would receive 7% each year, how much will
you have in 15 years? Using a linear equation to
graph it out, it would give you a better idea about
what how much you will have in the future.
• No matter what kind of situations, linear
equations help to make life easier.