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

I’m having a difficult time figuring this out. Can you please help me?-example-1

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5 votes

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

User Amrish Prajapati
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