1. W RITING E QUATIONS OF L INES Lesson 2.4

2. V OCABULARY Direct Variation: two variables x and y show direct variation provided y = kx where k is a nonzero constant. Constant of Variation: two nonzero constant (usually denoted as k) in a direct variation equation (y = kx) an inverse variation equation ( y = ) or a joint variation equation (z = kxy).

3. W RITING AN E QUATION OF A L INE Slope-Intercept Form: given the slope m and the y-intercept b this equationy = mx + b Point-Slope Form: given the slope m and a point (x 1, y 1 ) use this equationy – y 1 = m(x – x 1 ) Two Points: given two points (x 1, y 1 ) and (x 2, y 2 ) use the slope formula to find the slope m. Then use the point-slope form with this slope and either of the given points to write an equation of the line.

4. E XAMPLE 1: W RITING AN E QUATION G IVEN M AND B Write an equation of the line shown. A) B)

5. E XAMPLE 2: W RITING AN E QUATION G IVEN THE S LOPE AND A P OINT A) Write an equation of the line that passes through (1, 2) and has a slope of 2. B) Write an equation of the line that passes through (3, 5) and has a slope of 7.

6. E XAMPLE 3: W RITE E QUATIONS OF P ERPENDICULAR & P ARALLEL L INES Write an equation of the line that passes through (4, -1) and is A) Parallel to and B) Perpendicular to the line y =

7. E XAMPLE 4: W RITING AN E QUATION G IVEN T WO P OINTS A) Write an equation of the line that passes through (-1, 3) and (3, -2). B) Write an equation of the line that passes through (1, 5) and (4, 2).

8. E XAMPLE 5: W RITING AND U SING A D IRECT V ARIATION E QUATION A) The variables x and y vary directly and y = 15 and x = 5. Write and graph an equation relating x and y. Then find y when x = 3. B) The variables x and y vary directly and y = 4 and x = 24. Write and graph an equation relating x and y. Then find y when x = 12.