Question

Which equation shows the relationship in the table below X 3, 5, 8, 11 Y 7 ,11, 17, 23 a y=2xb y=x+4 c y=2x+1 d y=2x+4

Answer 1

ANSWER

$c)\text{ }y=2x+1$

EXPLANATION

We want to find the equation for the relationship shown in the table.

The relationship shown in the table represents a linear relationship. The general form of a linear equation is:

$y=mx+b$

where m = slope

b = y-intercept

To find the slope of the equation, apply the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

where (x1, y1) and (x2, y2) are two sets of values from the table.

Let us take (3, 7) and (5, 11) as (x1, y1) and (x2, y2)

Hence, the slope of the equation is:

$\begin{gathered} m=\frac{11-7}{5-3}=\frac{4}{2} \\ m=2 \end{gathered}$

Now, to find the equation of the line, apply the point-slope method:

$y-y_1=m(x-x_1)$

Therefore, the equation that shows the relationship in the table is:

$\begin{gathered} y-7=2(x-3) \\ y-7=2x-6 \\ y=2x-6+7 \\ y=2x+1 \end{gathered}$

The correct option is option C.