If 3 bricks weigh 9 pounds, 5 bricks weigh 15 pounds, and 8 bricks weigh 24 pounds, write an equation for the function and explain your variable choices.
How do I do this?
w = 3b
To solve this problem, we need to write an equation for the relationship between the number of bricks and their weight.
Let's start by identifying the variables we need to use. We can assign "x" as the number of bricks and "y" as the weight of the bricks.
From the given information, we have three data points:
- When 3 bricks are weighed, their weight is 9 pounds.
- When 5 bricks are weighed, their weight is 15 pounds.
- When 8 bricks are weighed, their weight is 24 pounds.
Based on these data points, we can establish a relationship between the number of bricks (x) and their weight (y). We observe that as the number of bricks increases by 2 (e.g., from 3 to 5 bricks), the weight increases by 6 pounds (e.g., from 9 to 15 pounds). From this pattern, we can deduce that for every increase of 2 bricks, the weight increases by 6 pounds.
So, the equation that represents this relationship is:
y = mx + b
To find the equation, we need to determine the values of "m" and "b."
The value of "m" represents the slope or the rate at which the weight changes as the number of bricks increases. In this case, the slope is 6 pounds per 2 bricks. Simplifying this ratio, we find the slope is 3 pounds per brick.
The value of "b" represents the y-intercept or the weight when there are 0 bricks. In this case, since we don't have the 0-brick weight given, we cannot determine the y-intercept. This means our equation will be in slope-intercept form, where we only know the slope.
Therefore, the equation for this function is:
y = 3x
This equation relates the weight (y) of the bricks to the number of bricks (x). Now, you can use this equation to find the unknowns in similar problems or solve for specific values.