if a large Factory sells its new gadgets for $5 each it can sell 1050 per month if it sells the same gadgets for $9 it will sell 900 per month assuming the relationship between prices and sales is linear predict the monthly sales of gadgets to the nearest whole number if the price is $12

788 Since we're assuming a linear relationship between sales and price, let's create an equation for the two points that we know. The general form of the equation will be in slope intercept form, so s = ap + b where s = number of sales a = slope of line p = price b = y intercept. So let's calculate a first. a = (1050 - 900)/(5-9) a = 150/(-4) a = -150/4 a = -37.5 So we now have the equation s = -37.5p + b Let's substitute one of out known price, sales pairs and solve for b. s = -37.5p + b 1050 = -187.5 + b 1237.5 = b So now we have the equation: s = -37.5p + 1237.5 Finally, just plug in the value 12 for p and calculate s. s = -37.5p + 1237.5 s = -37.5*12 + 1237.5 s = -450 + 1237.5 s = 787.5 And after rounding to the nearest whole number, we get 788.