2.3 Equations of Lines Going the other direction from a picture to the equation There are 3 standard forms of equations 1. Slope intercept form y y = mx + b slope intercept 2. Standard form Ax + By = C
A, B and C are integers and A is positive 3. Point slope form y y1 m(x x1 ) So, what do you need to have to find the equation of the line? Slope and Lets try one: a point
Slope=2 and the y-int = 5 y 2x 5 Find the equation of the line that has points of (0,3) and (4,0) y 3x 10 Slope = 3, x intercept = 10 y 3x 30 Slope = 3, passes through (10, 10) y 3x 20 6.Parallel to -4x + 2y = 10 and
passes through (-1, -1) m 2 1 2( 1) b y 2x 1 7. Parallel to x + 2y = 1 and passes through the point of intersection of the lines y = 3x Solve 2 and y =of 2x + 1. systems m 1/ 2
equations to get point! (3, 7) y 1/ 2x 8.5 Other Review Items Altitude Median M P Perpendicular bisector
Triangle ABC has vertices A(-4,-2) L(2,8) G(6,2) Write the equation of AL 8 ( 2) m Find the Slope: 2 ( 4) y 5 / 3x b 5 3
Plug in either point A or L 2 y 5 / 3x 4 3 Triangle ABC has vertices A(-4,-2) L(2,8) G(6,2) Find the equation of the perpendicular L bisector of LG. (4,5) Steps: 1.Find MP of LG (avg x, avg y)
G 2.Find the slope of LG and take neg reciprocal 2 mPlug 3. in MP to find b A 3 1 y 2 / 3x 2 3
Triangle ABC has vertices A(-4,-2) L(2,8) G(6,2) Find the equation of the altitude to AG L Steps: Find the slope of AG and take neg reciprocal 2. Plug in point L to find b m 5 2 A y 5 / 2x 13
G Group Problem: Find the distance between (0,4) and (3,0):