Equations for Lines Corresponds to Chapter 3.5 MCR

Slope-intercept form General format of 𝑦=𝑚𝑥+𝑏 Where m is the slope and b is the y-intercept The y-intercept should be written as a set of ordered pairs (0,b) This format is a convenient form to have when graphing a line

Point-slope General format is 𝑦− 𝑦 1 =𝑚(𝑥− 𝑥 1 ) This is the format to use to find the other equations when one point and the slope or two points are known.

An example—”I do” Given the set of points (2,3) and a slope of 1 2 , what is the equation of the line in point-slope form? 𝑦− 𝑦 1 =𝑚(𝑥− 𝑥 1 ) 𝑦−3= 1 2 (𝑥−2)

Standard form Standard form is 𝐴𝑥+𝐵𝑦=𝐶 Note there are no fractions in this format. This form is useful to find both the X and Y intercepts.

Example—”I do” Using the equation 𝑦−3= 1 2 𝑥−2 , change this to standard form 2 𝑦−3 =2[ 1 2 𝑥−2 ] (multiply both sides by 2) 2𝑦 −6=𝑥−2 (add 6 to both sides and also subtract an x) −𝑥+2𝑦=4 (finally, multiply both sides by -1) 𝑥−2𝑦=−4

Example—we do Write the equation of the line that goes through(8,4) & 4,1) in slope-intercept form The slope is 3 4 --now choose the easiest set of points (4,1) to put into the point-slope form 𝑦−1= 3 4 (𝑥−4) (now distribute) 𝑦−1= 3 4 𝑥−3 (add 1 to both sides) 𝑦= 3 4 𝑥 −2 (slope-intercept form). We could have just as easily put it in standard form.