Equations of Lines(rearranging the furniture)
There are three different forms of the equation of a line.
Two are for “show”:
slope-intercept equation of a line: y = mx + b
standard equation of a line: Ax + By = C
And one is a “workhorse”:
point-slope equation of a line: y – y1 = m( x – x1)
Three Forms of Linear Equations
The point-slope equation of a line: y – y1 = m( x – x1)
is used to figure out the equation of a line
when you are given a point and the slope.
You never give your answer in point-slope form.
Point-slope Equation of a Line
The slope-intercept equation of a line: y = mx + b
is great for graphing.
m is the slope of the line
(0, b) is the y-intercept of the line
You frequently are asked to give your answer in point-slope form.
Slope-intercept Equation of a Line
The standard equation of a line: Ax + By = C
is mainly for show.
You frequently are asked to give your answer in standard form.
Standard Equation of a Line
If they tell you that the slope is
And the y-intercept is (0, – 5)
The slope intercept equation is y = x – 5
Slope-intercept Form
7
4
7
4
The slope intercept equation is y = x – 5
To write that in standard form, first multiply each term by the LCD.
4y = 7x – 20
Then rearrange the furniture.
– 7x + 4y = – 20
7x – 4y = 20
From slope-intercept to Standard Form
7
4
Make x positive
What if they ask you to graph
7x – 4y = 20
Then rearrange the furniture – solve for y
– 4y = 7x – 20
y = x – 5
Now you know the slope and the y-intercept and it’s easy to graph!
From Standard to slope-intercept Form
7
4
Equations of lines
Point-slope: never the form of an answer.
Slope-intercept: Great for graphing. May be requested for an answer.
Standard form: Frequently requested for answers.