SOLUTION: How do you solve a question that says find the rate of change for each linear function?
Eg: The cost of cheese varies directly with the number of pounds bough. If 2 pounds cost
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Question 301230: How do you solve a question that says find the rate of change for each linear function?
Eg: The cost of cheese varies directly with the number of pounds bough. If 2 pounds cost $8.40, find the cost of 3.5 pounds.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Use the direct variation formula of y = k*x
Solve for k first using the known values of x and y.
Let x = 2 and y = 8.4
Formula becomes:
8.4 = k*2
Divide both sides of this equation by 2 to get:
k = 4.2
k winds up being the slope of your straight line equation.
The formula for a straight line equation is y = m*x + b
m is the slope and b is the y-intercept.
The slope is 4.2.
The y-intercept is found by substituting known values for x and y in the equation and solving for b.
the known values are (x,y) = (2,8.4)
Equation of y = 4.2*x + b becomes 8.4 = 4.2*2 + b which becomes 8.4 = 8.4 + b.
Solve for b to get b = 0.
Your straight line equation is y = 4.2*x
Graph this equation to get:
Horizontal line at y = 8.4 intersects the graph of the equation of the line at x = 2.
Horizontal line at y = 14.7 intersects the graph of the equation of the lin at x = 3.5.
This confirms the equation is good.
When x = 2, y = 8.4
When x = 3.5, y = 14.7
The rate of change is the slope of the line which is 4.2.
This means that for every change of 1 in the value of x, y changes by 4.2.
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