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

Answer:

6x-5y+3850=0

Step-by-step 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:

$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} (x-x_{1})$

Substitution:

$y-1370=\frac{1730-1370}{800-500} (x-500)\\\\y-1370=\frac{1360}{300} (x-500)\\\\Reducing\\\\y-1370=\frac{6}{5} (x-500)\\\\5(y-1370)=6(x-500)\\\\5y-6850=6x-3000\\\\6x-5y+3850=0$

clearing y:

$y=\frac{6}{5}x+770$

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