Question

What is the equation of the line graphed below?(2.1)O A. y = - 2xB. y = -2xC. y = 1/2D. y = 2x

Answer 1

The first step is to determine the slope of the line and that is calculated as follows;

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

Two points on the line have been identified as

$\begin{gathered} A=(0,0) \\ B=(2,1) \end{gathered}$

Note that the line passes through the origin which is (0, 0).

Therefore we now have;

$\begin{gathered} (x_1,y_1_{})=(0,0) \\ (x_2,y_2_{})=(2,1) \\ m=\frac{1-0}{2-0} \\ m=\frac{1}{2} \end{gathered}$

Now we have the slope determined as 1/2.

The y-intercept is derived as follows;

$\begin{gathered} \text{ Using the general equation of a straight line, which is;} \\ y=mx+b \\ b=y-\text{intercept} \\ We\text{ shall use point B=(2,1)} \\ 1=\frac{1}{2}(2)+b \\ 1=1+b \\ \text{Subtract 1 from both sides} \\ 0=b \end{gathered}$

We now have the values of m and b, the equation now becomes;

$\begin{gathered} y=mx+b \\ \text{Substitute for m=}\frac{1}{2},b=0 \\ y=\frac{1}{2}x+0 \\ y=\frac{1}{2}x \end{gathered}$

The correct answer therefore is option C