Point Slope Equation of a Line. Any time you are given the slope of a line (m) and a point on the line ( x 1, y 1 ) Use the point-slope equation of a.

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Presentation transcript:

Point Slope Equation of a Line

Any time you are given the slope of a line (m) and a point on the line ( x 1, y 1 ) Use the point-slope equation of a line to solve. y – y 1 = m ( x – x 1 )

Point Slope Equation of a Line m = 5; ( 2, 3 ) Use the point-slope equation of a line to solve. y – y 1 = m ( x – x 1 ) 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 form Ax + 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 – y 1 = m ( x – x 1 )

Oh no! A Fraction! y – y 1 = m ( x – x 1 ) Notice how I use parentheses to keep my signs straight!

Clean up the double signs

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

Fractions and Equal Signs

Finish Up! Answer in slope-intercept form

Finish Up! Answer in standard form with no leading negative.

Point- slope equation of a line 1.If you know a point ( x 1, y 1 ) and the slope m. 2.Use y – y 1 = m ( x – x 1 ) 3.Distribute the m 4.Move the y 1 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).