Question

A printing firm charged $35 for printing 600 sheets and $47 for printing 800 sheets find the formula assuming the relationship is linear

Answer 1

The formula expressing the relationship between the number of sheets printed and the cost charged by the printing firm is y = 0.06x - 1.

Step-by-step explanation:

The relationship between the number of sheets printed and the cost charged by the printing firm is assumed to be linear. We can find the formula to express this relationship using the given information.

Let's assign 'x' as the number of sheets and 'y' as the cost charged. We are given two data points: (600, $35) and (800, $47).

Using the formula for the equation of a line, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values from the data points to find the formula. First, let's find the slope:

m = (y2 - y1) / (x2 - x1) = (47 - 35) / (800 - 600) = 12 / 200 = 0.06

Next, let's find the y-intercept:

b = y - mx = 35 - (0.06 * 600) = 35 - 36 = -1

Therefore, the formula expressing the relationship between the number of sheets printed and the cost charged is y = 0.06x - 1.

Answer 2

Here, Coordinates are: (35, 600) & (47, 800)
Now, Slope (m) = y2 - y1 / x2 - x1
m = 800 - 600 / 47 - 35
m = 200 / 12 = 100 / 6
m = 50/3

Take any one coordinate into slope-intercept formula:
y - y1 = m(x - x1)
y - 600 = 50/3 (x - 35)
y - 600 = 50x/3 - 1750/3
y = 50x/3 + 50/3

In short, Your Answer would be: y = 50x/3 + 50/3

Hope this helps!