262 Chapter 3 Graphing Linear Equations in Two Variables y y1 m1x x12 y 142 33x 1224 m 3, x1 2, and y1 4. Apply the distributive property. Slope-intercept form y 4 3x 6 y 3x 2 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 (2, 4) y 3x 2 y x 1 2 3 4 5 5 4 3 2 1 1 2 3 4 5 Figure 3-30 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 y 5 13x 1224 m 1, x1 2, and y1 5. Substitute Simplify. y 5 11x 22 y 5 x 2 y x 3 12, 52 as 1x1, y12. m 1 m y2 y1 x2 x1 112 152 142 122 6 6 1 1x1, y12 1x2, y22 y mx b replace m, x, y 4 3122 b 4 6 b 2 b y mx b replace m, b Classroom Example: p. 267, Exercise 20 14, 12 for 1x1, y12 y y1 m1x x12 y 112 11x 42 y 1 x 4 Answer 2. y 2x 3 The point-slope formula: Substitute Simplify. Because the final answer is required in slope-intercept form, simplify the equation and solve for y. y 4 31x 22 Instructor Note: Show students an alternative method. y 3x 2 Skill Practice 2. Use the point-slope formula to write an equation of the line passing through the points (1,1) and (1,5). 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 1x1, y12.
miller_introductory_algebra_3e_ch1_3
To see the actual publication please follow the link above