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Geometry Unit IIB 3.7: Writing Equations of Lines

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Geometry. Unit IIB 3.7: Writing Equations of Lines. Coordinates of a point on a graph. =-1. ). Y. - PowerPoint PPT Presentation

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Page 1: Geometry

Geometry

Unit IIB3.7: Writing Equations of Lines

Page 2: Geometry

While the slope-intercept form for the equation of a line is very useful in graphing, it is not nearly as useful for writing the equation of a line (unless you happen to be given the slope and the y-intercept). The point-slope form for the equation of a line is _____________________________________

In this equation m is, again, the slope and x1 and y1 are _________________________________________

__________________________________

π‘¦βˆ’ 𝑦1=π‘š (π‘₯βˆ’π‘₯1)Coordinates of a point on a graph

Page 3: Geometry

Example: Write an equation for the line in point-slope form. 1. slope of -1 and contains the point (-3, 9) 2. passes through the points (1, 4) and (-3, 8)

3. slope of 3 and a y-intercept of 15 4. passes through the point (5, 1) and is perpendicular to the line π‘¦βˆ’15=3(π‘₯βˆ’0)

π‘¦βˆ’ 𝑦1=π‘š (π‘₯βˆ’π‘₯1)

π‘¦βˆ’ 𝑦1=π‘š (π‘₯βˆ’π‘₯1)

π‘¦βˆ’ 𝑦1=π‘š (π‘₯βˆ’π‘₯1))

π‘¦βˆ’9=βˆ’π‘₯βˆ’3𝑦=βˆ’π‘₯+6

=-1

π‘¦βˆ’4=βˆ’1(π‘₯βˆ’1)π‘¦βˆ’4=βˆ’π‘₯+1𝑦=βˆ’π‘₯+5

π‘¦βˆ’1=βˆ’3/5(π‘₯βˆ’5)π‘¦βˆ’15=3π‘₯𝑦=3 π‘₯+15

π‘¦βˆ’1=βˆ’35π‘₯+3

Page 4: Geometry

If you are specifically asked to write an equation in slope-intercept form, it is generally easiest to write it in point-slope form first and then change it to slope-intercept. Example: Write an equation of the line in slope-intercept form. 5. passes through the points (-4, 7) and (-2, 12) 6. passes through the point (12, 15) and is parallel to the line

π‘š=12βˆ’7βˆ’2+4

=52

𝑦=π‘šπ‘₯+𝑏

7=52

(βˆ’4 )+𝑏

7=βˆ’10+𝑏

17=𝑏

𝑦=52π‘₯+17

π‘¦βˆ’ 𝑦1=π‘š (π‘₯βˆ’π‘₯1)π‘¦βˆ’15=1 /3(π‘₯βˆ’12)

π‘¦βˆ’15=1 /3π‘₯βˆ’4

Y π‘¦βˆ’7=

52(π‘₯+4 )

π‘¦βˆ’ 𝑦1=π‘š (π‘₯βˆ’π‘₯1)

π‘¦βˆ’7=52π‘₯+10

𝑦=52π‘₯+17