Linear Equations and Slope Interpretation in Algebra
Understand linear equations, slopes, and intercepts in algebraic models through examples involving calculations, interpretations of slope meaning, y-intercepts, and x-intercepts in various scenarios. Explore how to compare costs, determine points of intersection, and analyze the implications of slopes in real-world applications.
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DO NOW Given the following data, find the slope, equation, and y- intercept. Describe the meaning of the and slope.
SECTION 1.3 MODELING WITH MATHEMATICS DAY 3 Algebra 2-Period 6
Ex 2: The equation h = - 3t + 48 represents a model of the height h, in inches, of water in a pool at time t in minutes. a) How can we determine the slope if we are not using x and y? b) What does the slope in represent? c) What does the y-intercept represent? d) What does the x-intercept represent?
You Do 1: The equation C = 240 + 25b is a linear model of the charge of a train ticket C if you bring b bags on the train. a) What does the slope represent? b) What does the y-intercept represent? c)Does the x-intercept make sense in this problem? Explain.
LINEAR SYSTEMS Two prom venues charge a rental fee plus a fee per student. The table shows the total costs for different numbers of students at Lakeside Inn. The total cost y (in dollars) for x students at the Sunview Resort is represented by the equation y = 10x + 600. Lakeside Inn Which venue charges less per student? Number of students, x 100 125 150 175 200 Total cost, y $1500 $1800 $2100 $2400 $2700 How many students must attend for the costs to be the same?
UNDERSTANDING THE PROBLEM 1. Create the equation for the Lakeside Inn: Slope: ? =1800 1500 125 100=300 25= 12 Equation: ? ?1= ?(? ?1) ? 1500 = 12 ? 100 ? 1500 = 12? 1200 ? = 12? + 300 2. Compare the slopes to see which is cheaper: Sunview charges $10 per student, Lakeside charges $12 per student. Sunview is cheaper. 3. Solve for when total cost is the same: 10? + 600 = 12? + 300 300 = 2? ? = 150 Total costs would be the same at 150 students.
You Do 2: Kelly and Kim are both babysitters. Kelly charges a flat fee of $10 plus $6 per hour to babysit. The table below shows the hourly fee that Kim charges to babysit. Who charges more per hour? number of hours, x 1 2 3 4 Total fee, y How many hours must Kim and Kelly babysit for their charges to be the same? $22 $26 $30 $34
HOMEWORK Function Review Packet # 3b, 5b, 6(a-c)
