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=(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=(6-2)/(4--2)=(4)/(4+2)=(4)/(6)=(2)/(3)`

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

`y-2=(2)/(3)(x--2)`
`y-2=(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