Forms of Linear Equations
Add yours
Key Questions

There are 4 forms of linear equations, they are:
 direct variation
 slopeintercept form
 standard form and
 pointslope form

We can use the x and yintercepts to graph linear equations in standard form (
#Ax+By=C# ).For example, let's graph
#3x+4y=12# .To find the xintercept we substitute 0 for y in the equation (every point on the xaxis has a ycoordinate of 0).
#3x+4(0)=12=>3x=12=>x=4# So, the xintercept is 4. Now let's find the yintercept by substituting 0 for x in the equation (similarly, every point on the xaxis has a ycoordinate of 0).
#3(0)+4y=12=>4y=12=>y=3# So, the yintercept is 3. We can now plot both points in the coordinate plane and draw a line through them.
See image below.

The standard form of linear equation is ax+by=c.
For example:
y = 5x + 2
To express this in standard form of linear equation just simply identify what's a, b, and c. And in this expression :
a= 5 ; b= 1 and c=2. Therefore, the standard form is 5x+y=2 (Note that the value of b become 3 because you need its subtraction property in order to substitute it). However, the value of "a" shouldn't be negative so you need to multiply it by 1 so the answer will be 5xy=2. 
The point slope form of an equation of a line is
#(yy_1)=m(xx_1)# where m is the slope and# (x_1,y_1)# is a point on the line.The standard form of the equation of a line is given as
#Ax+By=C# where A, B and C are all integers.Example: Change
#(y2)=5(x+3)# to standard form.First, we distribute 5 to each and every term inside the group at the right side;
#(y2)=5(x+3)#
#y2=5x+15# Note: Always make A positive in every standard form equationWe transpose y at the right side instead of 5x at the left, just to make A positive.Also, transpose 15 at the left side.
#215=5xy#
#17=5xy#
Through commutative property of equality, this equation is the same as#5xy=17# the standard form of the equation.Now, how we change point slope form to slope intercept form?
The slope intercept form of an equation of a line is given as
#y=mx+b# where m is slope and b is the y intercept.Given
#(y2)=5(x+3)# , change it to slope intercept formAgain, distribute 5 in each and every term inside the parenthesis at the right side of the equality.
#y2=5x+15# Then transpose 2 at the right side, the equation becomes
#y=5x+15+2# #y=5x+17# where m= 5 and b=17.Done!
Questions
Videos on topic View all (2)
Forms of Linear Equations

1Write an Equation Given the Slope and a Point

2Write an Equation Given Two Points

3Write a Function in SlopeIntercept Form

4Linear Equations in PointSlope Form

5Forms of Linear Equations

6Applications Using Linear Models

7Equations of Parallel Lines

8Equations of Perpendicular Lines

9Families of Lines

10Fitting Lines to Data

11Linear Interpolation and Extrapolation

12Problem Solving with Linear Models

13Dimensional Analysis