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260 Chapter 3 Linear Equations in Two Variables 6c. Write the equation of the line through (4, -1) that is perpendicular to y = 2x + 4. �������������������������������������� ���������������������������������������������������������������� The error was made in calculating the value of b. The y-intercept of the given line is (0, 4), but this is not necessarily the y-intercept of the perpendicular line. We must use the slopeintercept form or point-slope form to find the equation. Use m=- 1 2 and (4, -1) to get y = mx + b -1=- 1 2 (4) + b -1=-2 + b 1 = b So, the equation is y=- 1 2 x + 1. The slope of the given line is m 2. The slope of a perpendicular line is m=- 2 . b = 4. is y=- 2 x + 4 SUMMARY OF KEY CONCEPTS 1. If the slope and y-intercept of an equation are known, writing the equation that satisfies this information is immediate. The value of m and b are substituted into the slope-intercept form y = mx + b. 2. There are three other situations that provide enough information for an equation of a line to be written. They are: • a point and a slope • two points • a point and a line parallel or perpendicular In each of these situations, the slope must be determined. If it is not given, use the slope formula or the relationship to a given line to find it. After the slope is found, use it with one of the points in either the point-slope form or the slope-intercept form to write the equation of the line. 3. If a line is described as vertical or with undefined slope, the equation of the line will be of the form x = h, where h is the x-coordinate of the given point. 4. If a line is described as horizontal or with zero slope, the equation of the line will be of the form y = k, where k is the y-coordinate of the given point. 5. In application problems, we will either know the slope (how the values change) and y-intercept (initial value) from the problem or we will be given two points that enable us to write the equation. p g =2 Th l f perpendicu 1 The value of b So, the equation is 1 ANSWERS TO STUDENT CHECKS Student Check 1 a. y = -2x + 9 b. y = 7 3 x - 1 c. y = 2 3 d. y = 3 2 x + 1 Student Check 2 a. y = -5x + 16 b. y=- 2 7 x + 43 7 c. y = 9 d. x = 8 Student Check 3 a. y = -5x + 8 b. y=- 4 3 x + 2 3 c. y = -1 d. x = -8 Student Check 4 a. y = 1 2 x - 4 b. y = -2x + 1 c. x = 2 d. y = -3 Student Check 5 a. i. y = -3000x + 30,000 ii. $18,000 iii. 7 yr b. i. y = 0.54x + 15.3 ii. 21.78 million iii. 2024 GRAPHING CALCULATOR SKILLS The graphing calculator has the ability to calculate the equation of the line if provided enough information. At this point, it is more beneficial to use the calculator to check our work instead of allowing it to do the work for us. Example: Use the calculator to verify that y = 3 2 x + 6 is the equation of the line that goes through the points (-4, 0) and (4, 12).


hendricks_beginning_algebra_1e_ch1_3
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