Question

The cost for an order of 100 kilograms of steel bars is $230. The cost for an order of 150 kilograms of steel bars is $320. Write an equation for the cost of an order of steel bars (y) in terms of the weight of steel bars ordered (x). Show or explain how you found your equation.

Answer 1

To write an equation for the cost of an order of steel bars (y) in terms of the weight of steel bars ordered (x), use the given points to find the slope and substitute into the point-slope form of a linear equation.

Step-by-step explanation:

To write an equation for the cost of an order of steel bars (y) in terms of the weight of steel bars ordered (x), we can set up a linear equation using the given information.

We have two points:

(x1, y1) = (100, 230)

(x2, y2) = (150, 320)

We can use the formula for the equation of a line to find the equation:

slope (m) = (y2 - y1) / (x2 - x1)

Using the given points:

m = (320 - 230) / (150 - 100) = 90 / 50 = 1.8

Now we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), and substitute in one of the points:

y - 230 = 1.8(x - 100)

This is the equation for the cost of an order of steel bars (y) in terms of the weight of steel bars ordered (x).

Answer 2

y = 9x/5 + 50

Step-by-step explanation:

We are represent the information as coordinate (x,y)

If the cost for an order of 100 kilograms of steel bars is $230, this is expressed as (100, 230)

Also if the cost for an order of 150 kilograms of steel bars is $320, this is expressed as;

(150, 320)

Find the equation of a line passing through the points. The standard form of the equation is expressed as y = mx+c

m is the slope

c is the intercept

Get the slope;

m = y2-y1/x2-x1

m = 320-230/150-100

m = 90/50

m = 9/5

Get the y-intercept by substituting m = 9/5 and any point say (100, 230) into the expression y = mx+c

230 = 9/5(100)+c

230 = 9(20)+c

230 = 180 + c

c = 230-180

c = 50

Get the required equation

y = mx+c

y = 9/5 x + 50

Hence an equation for the cost of an order of steel bars (y) in terms of the weight of steel bars ordered (x) is y = 9x/5 + 50