Question

The following problem can be modeled with a linear equation. Analyze the problem and identify what quantities the variables x and y represent. The information provided in the problem is adequate to determine a point and a slope or two points on the line.

Robinson Wholesale Company paid $1370 for 500 items. Later they bought 800 items for $1730. Assume that the cost is a linear function of the number of items. Write the equation. (Let y represent the amount paid and x represent the number of items purchased.)

Answer 1

6x-5y+3850=0

Explanation:

If y represents the amount paid and x represents the number of items purchased, then the information provided is two points on the line:

`P_(1)(x_(1),y_(1))\\P_(2)(x_(2),y_(2))\\`

`P_(1)(500,1370)\\P_(2)(800,1730)\\`

We can find the equation with the next formulas:

having a point and a slope m:

`y-y_(1)=m(x-x_(1))\\`

having two points:

`y-y_(1)=(y_(2)-y_(1))/(x_(2)-x_(1)) (x-x_(1))\\`

Substitution:

`y-1370=(1730-1370)/(800-500) (x-500)\\\\y-1370=(1360)/(300) (x-500)\\\\Reducing\\\\y-1370=(6)/(5) (x-500)\\\\5(y-1370)=6(x-500)\\\\5y-6850=6x-3000\\\\6x-5y+3850=0`

clearing y:

`y=(6)/(5)x+770`

Where the slope m=6/5 and the intersection with y-axis is 770.