Final answer:
To find the linear equation representing yearly sales, calculate the slope from the provided data and use the sales in 1982 as the y-intercept to form the equation S = $9,900x + $8,500, with x being the years after 1982.
Step-by-step explanation:
The question asks us to find the equation that represents the yearly sales (S) of a certain appliance dealer, assuming the sales follow a linear function. The available data points are that sales were $8,500 in 1982 and $58,000 in 1987, with the year 1982 represented as zero (x=0).
To find the linear equation, we can use the format S = mx + b, where m is the slope of the line and b is the y-intercept. First, we calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), which represents the change in sales over the change in years.
Thus, m = ($58,000 - $8,500) / (1987 - 1982) = $49,500 / 5 = $9,900 per year. Next, we find the y-intercept (b), which is the initial amount of sales in 1982, so b = $8,500. Putting it all together, the equation for yearly sales is S = $9,900x + $8,500, where x is the number of years after 1982.
To find the equation giving yearly sales (S), we need to determine the slope and y-intercept of the linear function. We have two data points: $8500 in 1982 (year 0) and $58,000 in 1987 (year 5).
The slope can be found using the formula: slope = (change in S)/(change in year). Therefore, slope = (58000 - 8500)/(5 - 0) = 9900.
The y-intercept can be found by substituting one of the data points into the linear function. Let's use the point (0, $8500): $8500 = 0 * slope + y-intercept. Solving for y-intercept, we get: y-intercept = $8500.
Therefore, the equation giving yearly sales (S) is S = 9900(year) + $8500.