Question

I’m having a difficult time figuring this out. Can you please help me?

Answer 1

The Solution.

The equation of the line is given by the formula below:

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

Where m is the slope of the line, given as

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

Picking 2 points in the line, we have

$(-2,2)\text{ and (4,6)}$

That is,

$\begin{gathered} (x_1=-2,y_1=2) \\ (x_2=4,y_2=6) \end{gathered}$

So, finding the slope,m, we have

$m=\frac{6-2}{4--2}=\frac{4}{4+2}=\frac{4}{6}=\frac{2}{3}$

So, substituting into the formula for the equation of a line, we get

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

Cross multiplying, we get

$3(y-2)=2(x+2)$$3y-6=2x+4$$3y-2x=4+6$$3y-2x=10$$or\text{ 3y=2x+10}$

Therefore, the correct answer is 3y = 2x + 10 or 3y - 2x = 10