Section 3.5 Writing Equations of Lines 249 �� ������������������������ Writing Equations of Lines The average price of a movie ticket in the United States in 1996 was $4.42. The average price of a movie ticket in the United States in 2010 was $7.89. Write a linear equation that models the average price of a movie ticket. To answer this question, we need to know how to use two points to write the equation of a line. (Source: http://www.natoonline.org/ statisticstickets.htm) In Sections 3.1 to 3.4, we were given the equation of a line and we had to find certain information about it. In this section, we will be given specific information about a line and will write the equation of the line that satisfies the given conditions. The answers to these types of problems will be linear equations of the form y = mx + b or Ax + By = C. Use the Slope and y-Intercept to Write an Equation of a Line The first case we consider when writing equations of lines is when we are given a line’s slope and y-intercept. Recall that the slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. So, if we know the slope and y-intercept, we will substitute these values into the slope-intercept form to obtain the equation. ���������������������� Writing the Equation of a Line Given Its Slope and y-Intercept The line’s slope is the value of m and the y-coordinate of the y-intercept is the value b. So, the equation is y = ____ x + ____. �� ������������������������ ������������������ Write the equation of the line that satisfies the given information. 1a. m = 4 and the y-intercept is (0, 5) 1b. m=- 1 2 and the y-intercept is (0, -4) 1c. m = 0 and the y-intercept is (0, 1) 1d. Solutions 1a. The slope is m = 4 and the value of b = 5. So, the equation is y = 4x + 5 1b. The slope is m=- 1 2 and the value of b = -4. So, the equation is y = - 1 2 x - 4 Objective 1 ▶ Write the equation of a line given its slope and y-intercept. 2 2 4 6 –2 –2 –4 –6 x y ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Write the equation of a line given its slope and y-intercept. 2. Write the equation of a line given a point and a slope. 3. Write the equation of a line given two points. 4. Write the equation of a line given a point and a relationship to another line. 5. Solve application problems. 6. Troubleshoot common errors.
hendricks_beginning_algebra_1e_ch1_3
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