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) About Me  (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:

graph%28600%2C600%2C-5%2C5%2C-20%2C20%2C4.2%2Ax%2C8.4%2C14.7%29

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.