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 QUADRANT IV X-Axis
(-x, -y) (x, -y)
Y-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 Run 2
a dot on the point (0,-1).
Rise 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.
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.