Suppose you have $60 to buy shrimp and
chicken wings for a party. Shrimp costs $10/lb and wings cost $6/lb.
Write and graph a linear equation that could be used to determine the number of pounds of each food that can be purchased with $60
Would I start with the y = mx + b
60 = 10x + 6X + 0????
Nemo did it
read the top
pounds of shrimp --- x
pounds of wings ---- y
10x + 6y = 60
divide each term by 6
2x + y = 10 or y = -2x + 10
I will assume you know how to graph it
This is wrong you can't divide 10 by 6 !
To write a linear equation for this problem, let's define our variables:
Let x represent the number of pounds of shrimp to be purchased.
Let y represent the number of pounds of chicken wings to be purchased.
We know that shrimp costs $10 per pound and the chicken wings cost $6 per pound. Therefore, the cost of the shrimp can be calculated as 10x ($10 times the number of pounds of shrimp), and the cost of the wings can be calculated as 6y ($6 times the number of pounds of wings).
To determine the equation, we need to consider the total cost, which is given as $60. So, the equation can be written as:
10x + 6y = 60
This equation represents the total cost of buying shrimp and chicken wings, where the sum of the cost of the shrimp (10x) and the cost of the chicken wings (6y) equals $60.
Now, let's graph the equation to understand the solution visually:
To graph the linear equation, we need to rearrange it in the form y = mx + b, where m is the slope, and b is the y-intercept.
10x + 6y = 60 (original equation)
6y = -10x + 60 (subtracting 10x from both sides)
y = (-10/6)x + 10 (dividing both sides by 6)
Now, we have the equation in slope-intercept form. So the slope (m) is -10/6, and the y-intercept (b) is 10.
To graph this equation, plot the y-intercept of 10 on the y-axis, and then use the slope to find additional points. In this case, the slope of -10/6 means that for every 6 units of increase in x, the value of y decreases by 10 units.
Starting from the y-intercept of (0, 10), we can find additional points by using the slope:
For x = 6, y = (-10/6) * 6 + 10 = 0
For x = 12, y = (-10/6) * 12 + 10 = -10
Plot these points and draw a straight line connecting them. This line represents all the possible combinations of pounds of shrimp and chicken wings that can be purchased with $60.
Note: The graph may go beyond the positive quadrant in the fourth quadrant as well, but for this problem, non-negative values are only relevant.
I hope this explanation helps!