244 Chapter 3 Graphing Linear Equations in Two Variables Skill Practice 1. Use the point-slope formula to write an equation of the line having a slope of 4 and passing through (1, 5). Write the answer in slope-intercept form. The equation y 3x 2 from Example 1 is graphed in Figure 3-30. Notice that the line does indeed pass through the point (2,4). 54 321 5 4 3 2 1 1 2 3 4 2. Writing an Equation of a Line Given Two Points Example 2 is similar to Example 1; however, the slope must first be found from two given points. Writing an Equation of a Line Given Two Points Example 2 Use the point-slope formula to find an equation of the line passing through the points and Write the final answer in slope-intercept form. Solution: Given two points on a line, the slope can be found with the slope formula. Label the points. 12, 52 14, 12. 12, 52 and 14, 12 To apply the point-slope formula, use the slope, and either given point.We will choose the point y y1 m1x x12 12, 52 as 1x1, y12. y 5 13x 122 4 m 1, x1 2, and y1 5. Substitute Simplify. y 5 11x 22 y 5 x 2 y x 3 Skill Practice 2. Use the point-slope formula to write an equation of the line passing through the points (1,1) and (1,5). m 1 m y2 y1 x2 x1 112 152 142 122 6 6 1 1x1, y12 1x2, y22 14, 12 for 1x1, y12 1x1, y12. y y1 m1x x12 y 112 11x 42 y 1 x 4 Answers 1. y 4x 1 2. y 2x 3 (2, 4) y 3x 2 y x 1 2 3 4 5 5 Figure 3-30 TIP: The point-slope formula can be applied using either given point for In Example 2, using the point produces the same result. y x 3
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