Geometry

Unit IIB3.7: Writing Equations of Lines

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 _________________________________________

__________________________________

𝑦− 𝑦1=𝑚 (𝑥−𝑥1)Coordinates of a point on a graph

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 𝑦−15=3(𝑥−0)

𝑦− 𝑦1=𝑚 (𝑥−𝑥1)

𝑦− 𝑦1=𝑚 (𝑥−𝑥1)

𝑦− 𝑦1=𝑚 (𝑥−𝑥1))

𝑦−9=−𝑥−3𝑦=−𝑥+6

=-1

𝑦−4=−1(𝑥−1)𝑦−4=−𝑥+1𝑦=−𝑥+5

𝑦−1=−3/5(𝑥−5)𝑦−15=3𝑥𝑦=3 𝑥+15

𝑦−1=−35𝑥+3

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

𝑚=12−7−2+4

=52

𝑦=𝑚𝑥+𝑏

7=52

(−4 )+𝑏

7=−10+𝑏

17=𝑏

𝑦=52𝑥+17

𝑦− 𝑦1=𝑚 (𝑥−𝑥1)𝑦−15=1 /3(𝑥−12)

𝑦−15=1 /3𝑥−4

Y 𝑦−7=

52(𝑥+4 )

𝑦− 𝑦1=𝑚 (𝑥−𝑥1)

𝑦−7=52𝑥+10

𝑦=52𝑥+17