MSA Math Reflections p.45

1. A linear relationship represented by y=mx+b shows the relationship for the y-intercept in an equation, the point where the data line crosses the y-axis on a graph. In this equation, y depends on the x. b represents the point where the line crosses the y-axis, or when x=0. m represents the coefficient, or the number that a variable is multiplied by in an equation, so mx actually means m*x.

2a. A table or a graph for a linear relationship can be used to solve a problem because it shows you how the data changes over time. For example, if the student council were to purchase field day tee-shirts, they may check the prices of Store A and Store B. Store A charges $4.50 a shirt while Store B charges an initial down payment of $50 but only charges $1.50 a shirt. The table or a graph would be helpful because it would show how many shirts you would need to buy before the price is equal and how much is charged for that price. So instead of just looking at an equation, you would actually see how the data changes over time.

2b. One problem that I used an equation to solve was the problem with Fabian's bakery. The problem was "What are Fabian's monthly expenses and his monthly income for January if he sells 100 cakes that month?" There were two equations, one for the expenses and the other for income. The expense equation was E=825+3.25n, E represents the monthly expenses and n represents the number of cakes sold that month. The income equation was I=8.25n, with I representing the monthly income and n representing the number of cakes sold that month. To find the expenses and income, all that I needed to do was replace the n variable with 100 to stand for the 100 cakes sold, and the equation allowed me to find the month's expenses, $1,150, and the month's income, $820.