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Franklin Middle School is having a canned food drive. In Mr. Lao's class, Mr. Lao brought $10$ cans of food, and each student brought $2$ cans. In Ms. Roger's class, Ms. Rogers did not bring any cans, but each student brought $3$ cans of food. Write two equations in slope-intercept form to represent the number of cans of food for each class $y$ in terms of the number of students $x$ .

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Write equations of sine and cosine functions using properties

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Q. Franklin Middle School is having a canned food drive. In Mr. Lao's class, Mr. Lao brought

10

cans of food, and each student brought

2

cans. In Ms. Roger's class, Ms. Rogers did not bring any cans, but each student brought

3

cans of food. Write two equations in slope-intercept form to represent the number of cans of food for each class

y

in terms of the number of students

x

.

Mr. Lao's class equation: Let's start with Mr. Lao's class. We know that Mr. Lao brought $10$ cans of food, and each student brought $2$ cans. The number of cans of food $(y)$ is a function of the number of students $(x)$ . The equation will have a $y$ -intercept (where $x=0$ ) of $10$ , because that's the number of cans Mr. Lao brought. The slope of the equation will be $2$ , because each student brings $2$ cans. So the equation for Mr. Lao's class is: $\newline$ $y = 2x + 10$
Ms. Roger's class equation: Now let's consider Ms. Roger's class. Ms. Rogers did not bring any cans, so the $y$ -intercept is $0$ . Each student brought $3$ cans of food, so the slope of the equation is $3$ . The equation for Ms. Roger's class is: $\newline$ $y = 3x + 0$ $\newline$ which simplifies to: $\newline$ $y = 3x$

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