Question

The table and the graph below each show a different relationship between the same two variables, x and y: A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 3,240 and 4,320 and 5,400 and 6,480. On the right of this table is a graph. The x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis values on the graph are from 0 to 450 in increments of 90 for each grid line. A line passing through the ordered pairs 2, 90 and 4, 180 and 6, 270 and 8, 360 is drawn. How much more would the value of y be in the table than its value on the graph when x = 11? 110 150 385 450

Answer 1

The difference between value of y at x=11 is 385, the correct option is third.

Explanation:

The equation of a line which passing through two points is given below,

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

The two points from the table are (3,240) and (4,320), the equation is,

`y-240=(320-240)/(4-3)(x-3)`

`y-240=(320-240)/(4-3)(x-3)`

`y-240=80(x-3)`

`y=80x-240+240`

`y=80x`

Put x=11

`y=80* 11=880`

Therefore according to the table the value of y is 880 at x=11.

The two points from the table are (2,90) and (4,180), the equation is,

`y-90=(180-90)/(4-2)(x-2)`

`y-90=45(x-2)`

`y=45x-90+90`

`y=45x`

Put x=11,

`y=45* 11=495`

Therefore according to the table the value of y is 495 at x=11.

The difference between the values of y at x=11 is,

`D=880-495=385`

Therefore third option is correct.