Question

The scatter plot shows the number of customers in a restaurant for hours of the dinner services on two different Saturday nights. The line shown models this relationship, and x=0 represent 7:00pm

A. What does the value y-intercept represent in the context of the problem (shown inherent attachment)


B. What is the slope of the line?


C. Write an equation to represent the line of nest fit drawn


D. Wat is the number of customers the restaurant should expect at 8:30pm?

Answer 1

A. The value y-intercept represent in the context of the problem is 50.

B. The slope of the line is -10.

C. The equation to represent the line is y= -10x+50.

D. The number of customers in the restaurant at 8:30pm is 35.

Explanation:

The equation of the line is given by y=mx+c.

y is the number of customers and x is the hours.

7.00 p.m. is considered as 0.

To find the slope m =
`(rise)/(run).`

`rise = y_(2)-y_(1)`.

`run = x_(2)-x_(1)`.

From the graph, choose two points. Let us take (0,50) and (4,10).

`m=(-40)/(4).`

m=-10.

∴The equation can be written as y= -10x+c.

To find the y-intercept value c, substitute any point.

Let us substitute(0,50) for instance,

50=0+c.

c=50.

The equation for the given graph is y= -10x+50.

To find the customers at the restaurant at 8.30 pm.

we know that x=0 at 7.00 pm,

∴ x=1.5 can be considered as 8.30 pm.

Substitute x=1.5 in the line equation.

y= -10(1.5)+50.

y= -15-50.

y= 35.