Section 3.5 Point-Slope Formula 263 5 4 3 2 321 1 1 2 3 y x 3 11, 02 y 4x 3. y 4x 3 11, 02. 1x1, y12 11, 02. y y1 m1x x12 y 0 43x 1124 y 41x 12 y x 3 5 y 1 21 54 3 1 2 3 4 5 1 2 3 4 5 Writing an Equation of a Line Perpendicular to Another Line Example 4 Use the 1point-12 slope formula to find an equation of the line passing through the point 3, and perpendicular to the line 3x y 2. Write the final answer in slope-intercept form. Skill Practice 3. Use the point-slope formula 12 34 to write an equation of the line passing through (8, 2) and parallel to the line y x y 4x 4 Answer 3. y 3 4 x 4 3. Writing an Equation of a Line Parallel or Perpendicular to Another Line To write an equation of a line using the point-slope formula, the slope must be known. If the slope is not explicitly given, then other information must be used to determine the slope. In Example 2, the slope was found using the slope formula. Examples 3 and 4 show other situations in which we might find the slope. Writing an Equation of a Line Parallel to Another Line Use the point-slope formula to find an equation of the line passing through the point and parallel to the line Write the final answer in slope-intercept form. Solution: Figure 3-32 shows the line (pictured in black) and a line parallel to it (pictured in blue) that passes through the point The equation of the given line, is written in slopeintercept form, and its slope is easily identified as The line parallel to the given line must also have a slope of Apply the point-slope formula using and the point y 4x 4 m 4 4. 4. y 4x 3, Example 3 Figure 3-31 54 4 5 1 2 3 5 x 4 (2, 5) (4, 1) y Figure 3-32 x 4 3 2 (1, 0) y 4x 3 . Classroom Example: p. 267, Exercise 30 The solution to Example 2 can be checked by graphing the line using the slope and y-intercept. Notice that the line passes through the points ( 2, 5) and (4, 1) as expected. See Figure 3-31. TIP: When writing an equation of a line, slopeintercept form or standard form is usually preferred. For instance, the solution to Example 3 can be written as follows. Slope-intercept form: Standard form: 4x y 4
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