Point Slope Equation of a Line

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Point Slope Equation of a Line
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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 )
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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 )
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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 )
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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 form Ax By C just
rearrange the furniture! - 5x y -7
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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

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Oh no! A Fraction!
What if the slope is a fraction? M 2/3 ( -
7, - 5 ) We still use y y1 m ( x x1 )
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Oh no! A Fraction!
y y1 m ( x x1 ) Notice how I use
parentheses to keep my signs straight!
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Clean up the double signs

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Fractions and Equal Signs

Whenever you have a fraction and an equal
sign, multiply both sides of the equation by the
LCD.
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Fractions and Equal Signs

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Finish Up!

Answer in slope-intercept form
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Finish Up!

Answer in standard form with no leading negative.
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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).