During last night’s basketball game, Lisa Schmidt made 30 points in field goals. A field goal is worth 2 or 3 points.
If Lisa made 9 field goals worth 2 points each, how many did she make worth 3 points each?
Let x represent the number of 2-point field goals Lisa made and
y represent the number of 3-point field goals she made. Write an
equation to model the situation.
Plot several points to graph the equation.
Where does the line cross the x-axis? What does this point
represent in terms of Lisa’s points?
Where does the line cross the y-axis? What does this point
represent in terms of Lisa’s points?
To solve this problem, let's use the information given and create an equation that represents the situation.
We know that Lisa made 9 field goals worth 2 points each. We can express this as 2x, where x represents the number of 2-point field goals made.
We are also told that Lisa made a total of 30 points in field goals. If we let y represent the number of 3-point field goals made, then each 3-point field goal contributes 3y points.
So, our equation to model the situation is:
2x + 3y = 30
To plot several points and graph the equation, we can assign different values to x and solve for y by rearranging the equation.
Let's assign x = 0 and solve for y:
2(0) + 3y = 30
3y = 30
y = 10
So, one point on the graph is (0, 10).
Similarly, let's assign x = 1 and solve for y:
2(1) + 3y = 30
2 + 3y = 30
3y = 28
y = 9.33 (rounded to the nearest hundredth)
Another point on the graph is (1, 9.33).
We can repeat this process to find more points and plot them on a graph. Connecting these points will give us a line.
The line crosses the x-axis at a point where y = 0. Let's substitute y = 0 into the equation:
2x + 3(0) = 30
2x = 30
x = 15
So, the line crosses the x-axis at the point (15, 0). This point represents the number of 2-point field goals Lisa made without making any 3-point field goals.
Similarly, the line crosses the y-axis at a point where x = 0. Let's substitute x = 0 into the equation:
2(0) + 3y = 30
3y = 30
y = 10
So, the line crosses the y-axis at the point (0, 10). This point represents the number of 3-point field goals Lisa made without making any 2-point field goals.
In summary:
- The line crosses the x-axis at (15,0), representing the number of 2-point field goals Lisa made without making any 3-point field goals.
- The line crosses the y-axis at (0,10), representing the number of 3-point field goals Lisa made without making any 2-point field goals.
x=9
2x+3y = 30
Now the rest of the questions get easier.