Which of the following equations best, describes the linear relationship shown in the table, where g represents the number of pounds of grain sold and d represnets the price in dollars of one pound of grain ?

Options

A. `g=1.2d +12.500`
B. `g=12,500d+15,000`
C. `g =-12, 500d +17,500`
D. `g =- 12,500d+30,000`

Answer

D

Explanation

Take a quick peek at the answer choices. The equations are given in slope-intercept form, so start by finding the slop.e Substitute two pairs of values from the table (try to pick easy ones, if possible) into the slope formula, `m = (y _(1) -y_(1))/(x _(2) -x_(1)).` keep in mind that the projected number of pounds sold depends on the price, so the price is the independent variable (x) and the projected number is the dependent variable (x) and the project numbr is the dependent variable (y). Using the points `(1.2, 15,000) and (2.2,2,500),` you can find the slope:
`m = (2,500-15,000)/(2.2-1.2)`
`m= (-12,500)/(1)`
`m =- 12, 500`
This means you can eliminate (A) and (B) because the slope is not correct. Don't let (B) fool you-the project number of pounds sold goes down as teh price goes up, so there is an inverse relationship, which means the slope must be negative. To choose between (C ) and (D ), you could find the y-intercept of the line. Pick a point wiht easy values, such as `(2,5,000),` and plug in 5,000 for y and 2 for x:
`y=mx +b`
`5,000=-12,500(2) +b`
` 5,000=-25, 000+b`
` 30,000=b`
(D) is correct. Another oprion is to substitute `(2,5,000)` into (C ) and (D) only. Again, (D) is correct because `5,000=-12,500(2) +30,000` is a true stattement.