Point-Slope Form

b is not given, so we must find it Example 1 Find the equation of a line (slope-intercept form) passing through point (2, -3) with slope of -5 y = mx + b b is not given, so we must find it m is given (-5) What we Know: x = 2 y = -3 m = -5 Finding b: y = mx + b -3 = -5(2) + b -3 = -10 + b 7 = b Therefore: y = -5x + 7

b is not given, so we must find it Example 2 Find the equation of a line (slope-intercept form) passing through point (4, -1) with slope of 7 y = mx + b m is given (7) b is not given, so we must find it What we Know: x = 4 y = -1 m = 7 Finding b: y = mx + b -1 = 7(4) + b -1 = 28 + b -29 = b Therefore: y = 7x – 29

b is not given, so we must find it Example 3 Find the equation of a line (slope-intercept form) passing through point (-5, -3) with slope of 9 y = mx + b b is not given, so we must find it m is given (9) What we Know: x = -5 y = -3 m = 9 Finding b: y = mx + b -3 = 9(-5) + b -3 = -45 + b 42 = b Therefore: y = 9x + 42

b is not given, so we must find it Example 4 Find the equation of a line (slope-intercept form) passing through point (1, -2) with slope of 3 y = mx + b b is not given, so we must find it m is given (3) What we Know: x = 1 y = -2 m = 3 Finding b: y = mx + b -2 = 3(1) + b -2 = 3 + b -5 = b Therefore: y = 3x – 5

Using Point Slope Form y – y1 = m(x – x1)

Example 5 y – y1 = m(x – x1) Point Slope Form Find the equation of a line (slope-intercept form) passing through point (1, -2) with slope of 3 y – y1 = m(x – x1) Point Slope Form y – (-2) = 3(x – 1) Plug in values y + 2 = 3x – 3 Use distributive Property y = 3x – 5 Subtract 2

Example 6 y – y1 = m(x – x1) Point Slope Form Find the equation of a line (slope-intercept form) passing through point (3, 5) with slope of 6 y – y1 = m(x – x1) Point Slope Form y – 5 = 6(x – 3) Plug in values y – 5 = 6x – 18 Use distributive Property y = 6x – 13 Add 5

Example 7 y – y1 = m(x – x1) Point Slope Form Find the equation of a line (slope-intercept form) passing through point (-3, 5) with slope of -2 y – y1 = m(x – x1) Point Slope Form y – 5 = -2(x – (-3)) Plug in values y – 5 = -2(x + 3) Rewrite as y – 5 = -2x – 6 Use distributive Property y = -2x – 1 Add 5

Example 8 y – y1 = m(x – x1) Point Slope Form Find the equation of a line (slope-intercept form) passing through point (7, 8) with slope of -2 y – y1 = m(x – x1) Point Slope Form y – 8 = -2(x – 7) Plug in values y – 8 = -2x + 14 Use distributive Property y = -2x + 22 Add 8