Question

The table and the graph 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 3,180 and 4,240 and 5,300 and 6,360. 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 350 in increments of 70 for each grid line. A line passing through the ordered pairs 2, 70 and 4, 140 and 6, 210 and 8, 280 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
215
275

Answer 1

the answer is 275.

i got it right on my test.

Answer 2

The value of y be in the table is 275 more than its value on the graph when x = 11.

Explanation:

The slope represent the changer is y with respect to change in x.

`Slope=(y_2-y_1)/(x_2-x_1)`

From the table it is noticed that the value of y increased by 60 as the value of x increased by 1. Therefore the slope of the function is 60. It is also calculated by the formula. The two points from the table are (3,180) and (4,240).

`Slope=(240-180)/(4-3)=60`

The point slope form is,

`y-y_1=m(x-x_1)`

The equation of function is,

`y-180=60(x-3)`

`y-180=60x-180`

`y=60x`

Put x=11

`y=60* 11=660`

Therefore the value of table is 660 at x=11.

The two points from the graph are (2,70) and (4,140).

`Slope=(140-70)/(4-2)=35`

The equation of line is,

`y-70=35(x-2)`

`y-70=35x-70`

`y=35x`

Put x=11

Therefore the value of line is 385 at x=11.

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

`660-385=275`

Therefore the value of y be in the table is 275 more than its value on the graph when x = 11.