Writing Equations of Lines                                    -- Sections 2.2-2.3 -- Find the slope of the line that contains the points (-2, 3) and (1,-2).
 Solve Step Formula for slope given 2 points (x1, y1) and (x2, y2) y2 – y1 = -2 – 3 = -5 x2 – x1 = 1 – (-2) = 3 (-2, 3) and (1,-2) Done  Find the slope of the line that contains the points (1,-5) and (-4, 2). [Solution]  Find the equation of the line that contains the points (1,-2) and (2,-3). Solve Step Check  First find the slope using the slope formula You can check each point (1,-2)  x+ y = - 1 using the points (1,-2) and (2,-3) -2+ 1 = - 1 -1 = -1 y - y1 = m(x – x1) Now use point-slope form y – (-2) = -1(x – 1) Use either point (1,-2) (2,-3) y + 2 = -x + 1 Get x and y on the same side x+ y = - 1 x+ y = -1 Done Þ General Form 2+ (-3) = - 1 -1 = -1   Find the equation of the line that contains the points (-5,3) and (-4,1). [Solution]  Find the equation of the line that contains the point (1,-2)                                  and is perpendicular to the line 3x – 4y = -2 Solve Step Check 3x –  4y = -2 First find the slope of by solving for y You can check one point -4y = -3x – 2 Subtract 3x from both sides y = (-3/-4)x + 2/4 Divide by -4 (1,-2)  4x + 3y = -2 m = 3/4 The new slope will be the negative reciprocal of 3/4. (Section 2.2) 4(1) + 3(-2) = -2 4 – 6 = -2 So the new m = -4/3 Note: -2 = -2 y – (-2) = -4/3(x – 1) Now use point-slope form y - y1 = m(x – x1) 3(y + 2) = 3[-4/3(x – 1)] Multiply by 3 The fraction is gone now. 3y + 6 = -4(x – 1) 3y + 6 = -4x + 4 Get x and y on the same side 4x + 3y = -2 Done Þ  General Form  Find the equation of the line that contains the point (-1,3) and is                                    perpendicular to the line 3x + 5y = -6 [Solution]  A rare baseball card is expected to be worth \$ 690 after 3 years  and \$780 after 6 years.  What will the baseball card be worth after  8 years?  How much is the card worth today?
 This is an appreciation problem because the card is worth more after 6 years than after 3 years.   Let x = years and y = value in dollars Solve Step (3, 690) and (6,780) We have two points First find the slope using the slope formula using the points (3,690) and (6,780) y - y1 = m(x – x1) Now use point-slope form y – 690 = 30(x – 3) Use either point (3, 690) y – 690 = 30x – 90 Solve for y (slope-intercept form) y = 30x + 600 After 8 years Þ y = 30(8) + 600 = 240 + 600 = \$840    x = 8   Worth today Þ y = 30(0) + 600 = 0 + 600 = \$600       x = 0                         Note this is the y-intercept  Your car is expected to be worth \$ 15,000 after 1 years  and \$9,000 after 3 years.  What will the baseball card be worth after  5 years?  How much is the card worth today? [Solution] Tutorials and Applets by
Joe McDonald