Question

Find the equation for the trend line through the points (0, 11) and (100, 33). Then use it to predict the number of baskets Romy would make after practicing for 80 minutes.

Answer 1

28 baskets

Explanation:

The equation for a linear trend line is given by:

y = mx + b, where y and x are variables, m is the slope of the line and b is the y intercept (that is value of y when x is zero).

The equation of a line passing through two points
`(x_1,y_1)\ and\ (x_2,y_2)` is:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

y represent the number of baskets made and x represents the time take. Given that the line passes through the points (0, 11) and (100, 33), hence:

`y-11=(33-11)/(100-0)(x-0)\\\\y-11=(11)/(50)x\\\\y= (11)/(50)x+11`

The number of baskets Romy would make after practicing for 80 minutes (x = 80) is:

`y=(11)/(50)x+11\\\\y=(11)/(50)(80)+11 \\\\y=17.6+11\\\\y=28.6\\\\Therefore\ y\ =\ 28\ baskets`