Question

Which equation describes this line? (-2.4) O A. y - 4 = 3(x + 2) O B. y- 2 = 3(x – 4) O c. y - 4 = 3 (x - 2) D. y- 1 = 3(x - 18)

Answer 1

Since a single line passes through two points, then you can first obtain the slope of the line using the formula

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ \text{ Where m is the slope and the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}`

And then use the point-slope formula to find the equation of the line, that is

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

So, in this case, you have

`\begin{gathered} (x_1,y_1)=(-2,4) \\ (x_2,y_2)=(1,13) \end{gathered}`
`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ m=(13-4)/(1-(-2)) \\ m=(9)/(1+2) \\ m=(9)/(3) \\ m=3 \end{gathered}`

Now, using the point-slope formula

`\begin{gathered} y-4=3(x-(-2)) \\ y-4=3(x+2) \end{gathered}`

Therefore, the correct answer is A.

`y-4=3(x+2)`