Section 3.5 Writing Equations of Lines 257 ���������������������� Solving Problems Given an Initial Value and Rate of Change Step 1: Identify the initial (or beginning) value of the given quantity. This value represents b in the slope-intercept form of a line. Step 2: Identify how the initial value changes. This is the rate of change, or slope m. Step 3: Write the equation in slope intercept form y = mx + b by substituting the values of m and b into the equation. ���������������������� Solving Problems Given Two Data Points Step 1: Find the slope of the line between the two points. Step 2: Use one data point and the slope to determine the equation by using either the slope-intercept form or the point-slope form of a line. �� ������������������������ ������������������ Find the equation that represents each situation. Then use the equation to answer the questions. 5a. Juanita has just been hired as a public school teacher. Her starting salary is $35,000. She will get a raise of $1500 each year she works at the school. i. Write a linear equation that represents her salary, where x is the number of years worked. ii. Use the equation to determine Juanita’s salary after she has worked at the school for 10 yr. iii. Use the equation to determine how long she will have to work to have a salary of $80,000. Solution 5a. i. The starting salary is the initial value, so b = 35,000. The raise she gets each year is the rate of change or slope. m = change in y change in x = change in salary change in years = 1500 1 = 1500 The equation that models Juanita’s salary is y = 1500x + 35,000, where x is the number of years worked. ii. Juanita’s salary after working 10 years is found by setting x = 10. y = 1500x + 35,000 y = 1500(10) + 35,000 y = 15,000 + 35,000 y = 50,000 Begin with the model. Replace x with 10. Multiply. Add. So, Juanita’s salary after 10 yr is $50,000. iii. To determine how long she needs to work to have a salary of $80,000, we set y = 80,000. y = 1500x + 35,000 80,000 = 1500x + 35,000 80,000 - 35,000 = 1500x + 35,000 - 35,000 45,000 = 1500x 45,000 1500 = 1500x 1500 30 = x Begin with the model. Replace y with 80,000. Subtract 35,000 from each side. Simplify. Divide each side by 1500. Simplify. Juanita’s salary will be $80,000 after she works 30 yr at the school.
hendricks_beginning_algebra_1e_ch1_3
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