Question

(04.07A)

Answer 1

Answer:

The equation that best represents the relationship is $y=\frac{1}{2}x+2$.

Step-by-step explanation:

We are given the following table representing the two quantities below;

x        y

2       3

4       4

6       5

8       6

Firstly, we will find the two-point slope here, that is;

Consider two points; ($x_1,y_1$) = (2, 3) and ($x_2,y_2$) = (4,4)

Now, the formula for finding slope is;

Slope =  $\frac{y_2-y_1}{x_2-x_1}$

          =  $\frac{4-3}{4-2}$  =  $\frac{1}{2}$

Similarly, finding the slope for the points (6,5) and (8,6);

Slope =  $\frac{y_2-y_1}{x_2-x_1}$

          =  $\frac{6-5}{8-6}$  =  $\frac{1}{2}$

Now, the linear equation of the line having slope is given by;

$y-y_1=m\times (x-x_1)$  ; where m = slope and consider ($x_1,y_1$) = (2, 3)

So, the equation of the line is;

$y-3=\frac{1}{2} \times (x-2)$

$y-3=\frac{1}{2}x-1$

$y=\frac{1}{2}x+2$

Hence, the equation that best represents the relationship is $y=\frac{1}{2}x+2$.