The graph given shows the cost of sandwiches at a sandwich shop. Cost ($) 40 35 30 25 15 10 5 y 0 2 4 6 8 Number of sandwiches In the graph, y represents the cost of sandwiches and x represents the number of sandwiches sold. Which equation describes the proportional relationship between the cost of sandwiches and the number of sandwiches sold?
your choices are,
x = 10y
y = 5x
x = 5y
y = 10x
The proportional relationship between the cost of sandwiches and the number of sandwiches sold can be described by the equation y = 10x.
can you explain that
Certainly!
In the given graph, we have the cost of sandwiches (y) plotted on the vertical axis and the number of sandwiches sold (x) plotted on the horizontal axis.
To determine the equation that represents the proportional relationship between the cost and the number of sandwiches sold, we need to identify the relationship between the two variables.
From the graph, we can see that as the number of sandwiches sold increases, the cost of the sandwiches decreases. This means that there is an inverse relationship between the two variables, where as x increases, y decreases.
To find the equation, we can analyze the coordinates shown on the graph. Let's take two points: (5,2) and (10,0).
Using the slope formula: m = (y2 - y1) / (x2 - x1)
m = (0 - 2) / (10 - 5)
m = -2/5
Now that we have the slope, we can plug it into the point-slope form of a linear equation: y - y1 = m(x - x1)
Using the point (5,2), we have: y - 2 = (-2/5)(x - 5)
Simplifying the equation: y - 2 = (-2/5)x + 2
Now, we can rearrange the equation to solve for y (the cost of sandwiches):
y = (-2/5)x + 2 + 2
y = (-2/5)x + 4
So, the equation that represents the proportional relationship between the cost of sandwiches and the number of sandwiches sold is y = (-2/5)x + 4.
A singing competition is auditioning 45 contestants each hour for the next h hours. Which equation can be used to find the total number of contestants, C, that audition in h hours?
The equation that can be used to find the total number of contestants, C, that audition in h hours is C = 45h.
Explanation:
The given problem states that 45 contestants audition each hour. So, for each hour (h), there will be 45 contestants.
If we want to find the total number of contestants for h hours, we need to multiply the number of contestants per hour (45) by the number of hours (h). This can be represented by the equation C = 45h.
i figured out the question myself, and got 45h = C, would that be correct or incorrect?
Apologies for the confusion in my previous response. You are correct, the equation should be 45h = C.
The equation 45h = C reflects that there are 45 contestants auditioning per hour, and the total number of contestants C is determined by multiplying the number of hours h by 45. Each hour adds 45 contestants to the total count.
Well done on figuring it out!