tres chic boutique sold 500 handbags in 2010, and in 2015 they sold 1400 handbags. a. write an equation for…

tres chic boutique sold 500 handbags in 2010, and in 2015 they sold 1400 handbags. a. write an equation for the number of handbags sold, y, in terms of x, the number of years since 2010. y = b. how many handbags were sold in 2018? handbags c. what is the y - intercept? (0, ) what does it represent? select an answer d. in what year will 2120 handbags be sold?

tres chic boutique sold 500 handbags in 2010, and in 2015 they sold 1400 handbags. a. write an equation for the number of handbags sold, y, in terms of x, the number of years since 2010. y = b. how many handbags were sold in 2018? handbags c. what is the y - intercept? (0, ) what does it represent? select an answer d. in what year will 2120 handbags be sold?

Answer

Explanation:

Step1: Find the slope

The two - point form of a line is based on two points ((x_1,y_1)) and ((x_2,y_2)). Here, (x_1 = 0) (corresponding to 2010, so (y_1=500)) and (x_2 = 2015 - 2010=5), (y_2 = 1400). The slope (m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{1400 - 500}{5}=\frac{900}{5}=180).

Step2: Write the equation of the line

The slope - intercept form of a line is (y=mx + b), where (m) is the slope and (b) is the y - intercept. Since when (x = 0) (year 2010), (y = 500), (b = 500). So the equation is (y=180x + 500).

Step3: Find the number of handbags in 2018

For 2018, (x=2018 - 2010 = 8). Substitute (x = 8) into the equation (y=180x+500), then (y=180\times8 + 500=1440+500=1940).

Step4: Identify the y - intercept

The y - intercept is the value of (y) when (x = 0). From the equation (y=180x + 500), when (x = 0), (y = 500). It represents the number of handbags sold in 2010.

Step5: Find the year when 2120 handbags are sold

Set (y = 2120) in the equation (y=180x+500). Then (2120=180x + 500). Subtract 500 from both sides: (2120−500=180x), so (1620 = 180x). Solve for (x): (x=\frac{1620}{180}=9). The year is (2010 + 9=2019).

Answer:

a. (y = 180x+500) b. 1940 c. ((0,500)); The number of handbags sold in 2010 d. 2019