Section 2.3 Equations of a Line 163 Finding an Equation of a Line Given Two Points Example 6 Find an equation of the line passing through the points (5, 1) and (3, 1). Write the answer in slope-intercept form. Solution: The slope formula can be used to compute the slope of the line between two points. Once the slope is known, the point-slope formula can be used to find an equation of the line. m y y1 m1x x12 y2 y1 x2 x1 1 112 3 5 y 1 11x 32 m 1 y 1 x 3 y x 4 2 2 1 TIP: In Example 6, the point (3, 1) was used for (x1, y1) in the point-slope formula. However, either point could have been used. Using the point (5, 1) for (x1, y1) produces the same final equation: y 112 11x 52 y 1 x 5 Finding an Equation of a Line Parallel to Another Line Find an equation of the line passing through the point and parallel to the line Write the answer in slope-intercept form. Solution: To find an equation of a line, The known point is 1 2, 32. we must know a point on the line and the slope. Because the line is parallel to 4x y 8, the two lines must have the same slope. Writing the equation in slopeintercept form, we have Therefore, the slope of both lines must be 4. y 4x 8. 4x y 8 4x y 8. 12, 32 Example 7 y x 4 First find the slope. Next, apply the point-slope formula. Substitute and use either point for (x1, y1).We will use (3, 1) for (x1, y1). Clear parentheses. Solve for y.The final answer is in slopeintercept form. Skill Practice 8. Use the point-slope formula to write an equation of the line that passes through the points and 1 Write the answer in slope-intercept form. 1 1, 12. 5, 22 TIP: In Example 6, once the slope is found from the two given points, we can alternatively use slopeintercept form to find an equation of the line. Substitute the coordinates from either known point for x and y. Using the point (3, 1), we have: y mx b 1 1(3) b 1 3 b 4 b Therefore, y x 4. Answer 8. y 3 4 x 7 4
miller_intermediate_algebra_4e_ch1_3
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