Question

The table represents the total miles traveled, y, after a number of hours, x. Hours, x Miles, y 2.5 150 4.0 240 5.5 330 7.0 420 Which linear equation represents the situation?

Answer 1

(2.5,150)(4,240)
slope = (240 - 150) / (4 - 2.5) = 90 / 1.5 = 60

y = mx + b
slope(m) = 60
(4,240)...x = 4 and y = 240
now we sub and find b, the y int
240 = 60(4) + b
240 = 240 + b
240 - 240 = b
0 = b

so ur equation is : y = 60x + 0 which is written as : y = 60x <==

Answer 2

y = 60x is the required linear relation.

Explanation:

We are given the following information in the question:

Hours(x): 2.5 4.0 5.5 7.0

Miles(y): 150 240 330 420

We need to find a linear equation that represents the above scenario.

The linear equation can be calculated with the help of two-point form of straight line give by:

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

where,
`(x_1,y_1), (x_2,y_2)` are points on line.

Putting the values

`(x_1,y_1) = (2.5,150), (x_2,y_2) = (4,240)`

`(y-150) = \displaystyle(240-150)/(4-2.5)(x-2.5)\\\\(y-150) = \displaystyle(90)/(1.5)(x-2.5)\\\\1.5(y-150)=90(x-2.5)\\\\1.5y-225 = 90x-225\\1.5y = 90x\\y = 60x`

y = 60x is the required linear relation.