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

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4

7

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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

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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

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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.