Point Slope Equation of a Line

Point Slope Equation of a Line

Any time you are given the slope of a line (m)and a point on the line ( x1, y1 )

Use the point-slope equation of a line to solve.

y – y1 = m ( x – x1 )

Point Slope Equation of a Line

m = 5; ( 2, 3 )

Use the point-slope equation of a line to solve.

y – y1 = m ( x – x1 )

y – 3 = 5 ( x – 2 )

Slope-intercept Equation of a Line

y – 3 = 5 ( x – 2 )y – 3 = 5x – 10

y = 5x – 7

This is the slope-intercept equation of the line with a slope of 5 passing through the point ( 2,

3 )

Standard Equation of a Line

y = 5x – 7 This is the slope-intercept equation of the line

with a slope of 5 passing through the point ( 2, 3 )

If they want the answer in standard formAx + By = C

just rearrange the furniture!

- 5x + y = -7

A matter of style

- 5x + y = -7

Some textbook authors dislike starting with a negative.

Although this is a correct answer, if it is not included in the multiple choice answers, clean it

up by multiplying everything by -1.

5x – y = 7

Oh no! A Fraction!

What if the slope is a fraction?

M = 2/3 ; ( - 7, - 5 )

We still use y – y1 = m ( x – x1 )

2( 5) [ ( 7)]

3y x

Oh no! A Fraction!

y – y1 = m ( x – x1 )

Notice how I use parentheses to keep my signs straight!

2( 5) [ ( 7)]

3y x

Clean up the double signs

2( 5) [ ( 7)]

3y x

25 [ 7]

3y x

Fractions and Equal Signs

Whenever you have a fraction and an equal sign,

multiply both sides of the equation by the LCD.

25 [ 7]

3y x

Fractions and Equal Signs

25 [ 7]

32

3( 5) 3( )[ 7]3

3 15 2 14

y x

y x

y x

Finish Up!

3 15 2 14

3 2 1

2 1

3 3

y x

y x

y x

Answer in slope-intercept form

Finish Up!

Answer in standard form with no leading negative.

3 2 1

2 3 1

2 3 1

y x

x y

x y

Point- slope equation of a line

1. If you know a point ( x1, y1 ) and the slope m.

2. Use y – y1 = m ( x – x1 )

3. Distribute the m

4. Move the y1

5. This gives the slope-intercept equation of the line.

6. If they want it in standard form, rearrange the furniture ( and you may have to clear a leading negative).