Section 3.5 Point-Slope Formula 243 Point-Slope Formula Section 3.5 1. Writing an Equation of a Line Using the Point-Slope Formula In Section 3.4, the slope-intercept form of a line was used as a tool to construct an equation of a line. Another useful tool to determine an equation of a line is the point-slope formula. The point-slope formula can be derived from the slope formula as follows: Suppose a line passes through a given point and has slope m.If is any other point on the line, then: 1x1, y12 1x, y2 Slope formula Clear fractions. m m1x x12 y y1 x x1 y y1 x x1 m1x x12 y y1 1x x12 y y1 m1x x12 Point-slope formula Point-Slope Formula The point-slope formula is given by y y1 m1x x12 where m is the slope of the line and 1x1, y12 is any known point on the line. Example 1 demonstrates how to use the point-slope formula to find an equation of a line when a point on the line and slope are given. Writing an Equation of a Line Using the Point-Slope Formula Example 1 Use the point-slope formula to write an equation of the line having a slope of 3 and passing through the point Write the answer in slope-intercept form. Solution: The slope of the line is given: A point on the line is given: The point-slope formula: y y1 m1x x12 12, 42. m 3 1x1, y12 12, 42 y 142 33x 122 4 m 3, x1 2, and y1 4. Substitute Simplify. Because the final answer is required in slope-intercept form, simplify the equation and solve for y. Apply the distributive property. y 4 31x 22 y 4 3x 6 y 3x 2 Slope-intercept form Concepts 1. Writing an Equation of a Line Using the Point-Slope Formula 2. Writing an Equation of a Line Given Two Points 3. Writing an Equation of a Line Parallel or Perpendicular to Another Line 4. Different Forms of Linear Equations: A Summary
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