This document provides examples of writing equations of lines in slope-intercept form (y=mx+b). It demonstrates how to find the slope (m) and y-intercept (b) and write the equation based on: 1) A given slope and y-intercept. 2) Two points on the line. 3) A point and being parallel to another line. 4) A point and being perpendicular to another line. Formulas for finding slope and using point-slope form are also reviewed.

1. Writing Equations of Lines y = mx + b

2. y = mx + b m = ? b = ? b = -3 y = 2x - 3 Writing Equations of Lines +2 +2 +1 m = = 2 2 1 +1 y-intercept

3. y = mx + b Writing Equations of Lines Find the equation of the line with a slope of –2/3 and a y-intercept of 1 Find the equation of the line with a slope of –2/3 and a y-intercept of 1 y = x + 1 2 3 y = mx + b +2 -3 +3 -2 y = mx + b y = x + 1 2 3

4. Writing Equations of Lines Find the equation of the line through the points (-3,-4) and (3,-1). m = ? b = ? y = m x + b Change in y Change in x m = y 2 – y 1 x 2 – x 1 -1 – - 4 3 – - 3 = m = 3 6 = 1 2 m = 1 2 -1 = (3) + b 1 2 -1 = + b 3 2 5 2 = b b = 5 2 y = x – 1 2 5 2

5. Writing the Equation of a Line rise run Slope = = 5 3 y = mx + b (4,3) 3 = 5/3(4) + b 3 = 20/3 + b -20/3 -11/3 = b -3.67 = b y = 5/3x – 11/3

6. Writing Equations of Lines Find the equation of the line through the points (1,-2) and (-4,1). Point – Slope Form y – y 1 = m(x – x 1 ) derived from We still need the slope -2 -2 Check it out on the calculator m = y 2 – y 1 x 2 – x 1 m = 1 – - 2 -4 – 1 3 5 = y – - 2 = (x – 1) 3 5 y – - 2 = x + 3 5 3 5 y = - x – 3 5 7 5

7. Writing Equations of Lines Write the equation of the line through The point (1, 2) and parallel to the line Y = 1/3x – 4. m = ? y – 2 = 1/3(x – 1) y – 2 = 1/3x – 1/3 +2 +2 y = 1/3x + 5/3 m = 1/3 m = y 2 – y 1 x 2 – x 1

8. Writing Equations of Lines Find the equation of the line through The point (-3, -4) and perpendicular to the Line y = -2x + 1. y + 4 = 1/2(x + 3) y + 4 = 1/2x + 3/2 -4 -4 y = 1/2x – 5/2 m = ? m = 1/2 m = y 2 – y 1 x 2 – x 1