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 ID: 488554
Download Presentation The PPT/PDF document "Linear Equations" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Linear Equations
By:
Emily ZhouSlide2
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.Slide3
Parts of a Coordinate Plane
Origin
Y-Axis
X-Axis
QUADRANT II
(-x, y)
QUADRANT I
(x, y)
QUADRANT III
(-x, -y)
QUADRANT IV
(x, -y)Slide4
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.Slide5
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 =CSlide6
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.Slide7
Graph Using Slope Intercept Form
I will use the equation
y= ½ x-1
to demonstrate howto 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.
Rise 1
Run 2Slide8
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=41.) Substitute in a zero for x. Simplify. 2(0)+2y=4 y=22.) One point of the line is (0,2). Plot the point.3.) Substitute y with zero. Simplify. 2x+2(0)=4 x=24.) The second point is (2,0). Plot it and draw a line through the two points.Slide9
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.