Question

This table represents a relationship between x and y, where x is the independent variable. 1 2 3 4 5 y 6 7 00 9 10 Which equation represents the relationship between x and y? O x = y +5 o y = 5x O x= 5y O y = x + 5

Answer 1

We are given a table between two variables x and y.

Recall that the equation of a linear relationship is given by

$y=mx+b$

Where m is the slope and b is the y-intercept.

The slope is given by

$m=\frac{y_2−y_1}{ x_2−x_1}$

Let us select two (x, y) pairs from the given table

Let us select (1, 6) and (2, 7)

$\text{where}(x_1,y_1)=(1,6)\text{and}(x_2,y_2)=(2,7)$

Let us substitute these values into the slope formula

$m=\frac{y_2−y_1}{x_2−x_1}=\frac{7-6}{2-1}=\frac{1}{1}=1$

So, the slope is 1 and the equation becomes

$y=x+b$

Now let us find the y-intercept (b)

Let us select any one (x, y) pair from the given table.

Let us select (1, 6) and substitute it into the above equation

$\begin{gathered} y=x+b \\ 6=1+b \\ 6-1=b \\ 5=b \\ b=5 \end{gathered}$

Therefore, the equation is

$y=x+5$

The last option is the correct answer.