The Standard Form of a Linear Equation
The Standard Form of a Linear Equation is in the form
Ax + By = C
A, B, and C are numbers and (x, y) are a point on the line.
An example of this form would be 6x + 3y = 18. You cannot tell the slope, y-intercept, or a point on the line from this form, but you can easily convert it to Slope-Intercept Form by solving for y.
6x + 3y = 18 standard form
-6x -6x subtract 6x from both sides
3y = -6x + 18
3 3 3 divide all terms by 3
y = -2x + 6 Slope-Intercept Form
Now we can see that the slope= -2 and the y-intercept =6.
Try this interactive website to see how manipulating the line changes the Standard Form of the equation: http://www.geogebra.org/en/upload/files/english/Athena_Matherly
/Standard_Form/standard_form_WS.html
The video below shows the relationship between all the forms of linear equations:
Ax + By = C
A, B, and C are numbers and (x, y) are a point on the line.
An example of this form would be 6x + 3y = 18. You cannot tell the slope, y-intercept, or a point on the line from this form, but you can easily convert it to Slope-Intercept Form by solving for y.
6x + 3y = 18 standard form
-6x -6x subtract 6x from both sides
3y = -6x + 18
3 3 3 divide all terms by 3
y = -2x + 6 Slope-Intercept Form
Now we can see that the slope= -2 and the y-intercept =6.
Try this interactive website to see how manipulating the line changes the Standard Form of the equation: http://www.geogebra.org/en/upload/files/english/Athena_Matherly
/Standard_Form/standard_form_WS.html
The video below shows the relationship between all the forms of linear equations:
__If the video above is not working, you need to download the Adobe Flash player.
Here are some more examples: http://courses.wccnet.edu/~palay/precalc/22mt01.htm
PRACTICE
This website has lots of problems to practice with: http://www.algebralab.org/studyaids/studyaid.aspx?file=algebra1_5-5.xml
ASSESS
Think you have it? Try this quiz: http://www.mathsisfun.com/quiz/linear_equation_test.html Post your score in the Interactive Assessment Scores forum below.
Now try writing the equations of Horizontal and Vertical Lines.
Here are some more examples: http://courses.wccnet.edu/~palay/precalc/22mt01.htm
PRACTICE
This website has lots of problems to practice with: http://www.algebralab.org/studyaids/studyaid.aspx?file=algebra1_5-5.xml
ASSESS
Think you have it? Try this quiz: http://www.mathsisfun.com/quiz/linear_equation_test.html Post your score in the Interactive Assessment Scores forum below.
Now try writing the equations of Horizontal and Vertical Lines.