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

Answer:

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

Step-by-step explanation:

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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

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

$y-240=\frac{320-240}{4-3}(x-3)$

$y-240=\frac{320-240}{4-3}(x-3)$

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

$y=80x-240+240$

$y=80x$

Put x=11

$y=80\times 11=880$

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,

$y-90=\frac{180-90}{4-2}(x-2)$

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

$y=45x-90+90$

$y=45x$

Put x=11,

$y=45\times 11=495$

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.

Answer 2

To determine the equation of line, we need two points that is passing through the line. Thus, the value of y is 495 when x is equal to 11.

A line passing through the ordered pairs 2, 90 and 4, 180 and 6, 270 and 8, 360.

Thus, the points that is lie on the line is (2,90) and (4,180).

The equation of line passing through the two points (x1,y1) and (x2,y2) can be formulated as:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1} (x-x_1)$

There, substitute the values and solve it further.

$y-90=\dfrac{180-90}{4-2} (x-2)\\y-90=45(x-2)\\y-90=45x-90\\y=45x$

Thus, substitute the value of x=11 in above equation.

$y=45 \times 11\\y=495$

Therefore, when x=11, the value of y is 495.

To know more about the equation of the line, please refer to the link:

https://brainly.com/question/20632687