Lesson 5.6 Point-Slope Form of the Equation of a Line

Point-Slope Form of the Equation of a Line A line that passes through the point (x1, y1) with a slope of m. The point-slope form of the equation of the line is: y – y1 = m(x – x1) There is a difference between (x1, y1) and (x, y). (x1, y1) is a specific point on the line. (x, y) represents ANY point on a line.

A line is passing through the points (-3, 6) and (1, -2) A line is passing through the points (-3, 6) and (1, -2). Write the equation of a line in Point-Slope Form. Step 1: Find the slope. m = y2 -y1 = -2 – 6 = -8 = -2 x2-x1 1 – -3 4 Step 2: Substitute one point, (-3, 6) and the slope into the Point-Slope Form equation: y – y1 = m(x – x1) y – 6 = -2(x - -3) y – 6 = -2(x + 3)

Change from Point-Slope Form to Slope-Intercept Form Write an equation of the line that passes through (2, 3) with a slope of – ½ . Substitute into Point-Slope Form. y – y1 = m(x – x1) y – 3 = - ½(x – 2) Simplify the equation to put it into slope-intercept form. y – 3 = - ½x + 1 y = - ½x + 4

Which equation would you use Which equation would you use? Slope-Intercept, Standard, or Point-Slope Form The line passes through the points (1, 3) and (-2, 4). Point-slope because a point is given and a slope can be determined. The line has a slope of -4 and has a y-intercept of -12. Slope-intercept form because a slope and the y-intercept are given.