In order to write the combinations, choose points that lie on the line. Remember that the numbers of T-shirts and sweatshirts must be whole numbers.
Equation: 12x+15y=120 Graph:
Combinations:
Number of T-shirts
Number of Sweatshirts
0 T-shirts
8 Sweatshirts
5 T-shirts
4 Sweatshirts
10 T-shirts
0 Sweatshirts
Practice makes perfect
Let x represent the number of T-shirts and y represent the number of sweatshirts that we buy. We know that one T-shirt costs $12 and one sweatshirt costs $15. If we plan to spend $120, we can write some expressions to represent our data.
Verbal Expression
Algebraic Expression
Cost of x T-shirts
$12* x
Cost of y sweatshirts
$15* y
Add the costs of T-shirts and sweatshirts
$12* x+ $15* y
Form the equation
$12* x+ $15* y= $120
Thus, the equation is the following.
12x+ 15y= 120Now we will find the interception points of the equation to graph it. Let's start with the x-intercept. In order to find the x-intercept, we will substitute 0 for y and solve the equation for x.
Thus, the y-intercept is the point (0,8). Next, we will plot the interception points and graph the equation by connecting them.
As a final step, we will choose three points that lie on the line to write 3 combinations of possible purchases. Remember that the number of T-shirts and sweatshirts must be whole numbers.
