Question

Answer if u love cats & dogs

Answer 1

Answer:

(7, 5.25) lies on the graph.

Step-by-step 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:

$m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}$

Now, the equation of line becomes:

$y=\dfrac{3}{4}x+c$

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

$3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0$

So, final equation of given function is:

$y=\dfrac{3}{4}x$

OR

$4y=3x$

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

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