Question

Answer if u love cats & dogs

Answer 1

(7, 5.25) lies on the graph.

Explanation:

We are given the following values

x = 4, 6, 8, 12 and corresponding y values are:

y = 3, 4.5, 6, 9

Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.

Equation of a line passing through two points
`(x_1,y_1)` and
`(x_2,y_2)` is given as:

`y=mx+c`

where m is the slope.

(x,y) are the coordinates from where the line passes.

c is the y intercept.

Here,

`x_(1) = 4\\x_(2) = 6\\y_(1) = 3\\y_(2) = 4.5`

Formula for slope is:

`m = (y_(2)-y_(1))/(x_(2)-x_(1))`

`m = (4.5-3)/(6-4)\\\Rightarrow m = (1.5)/(2)\\\Rightarrow m = (3)/(4)`

Now, the equation of line becomes:

`y=(3)/(4)x+c`

Putting the point (4,3) in the above equation to find c:

`3=(3)/(4)* 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0`

So, final equation of given function is:

`y=(3)/(4)x`

OR

`4y=3x`

As per the given options, the point (7, 5.25) satisfies the equation.

So correct answer is
`(7, 5.25)`.