Question

Which equation represents a line that passes through the two points in thetable?хy3166A. y-6=3/5(x-6)B. y+1=5/3(x+3)C. y+6=3/5(x+6)D. y-1=5/3(x-3)

Answer 1

To obtain the equation of the line that passes through these points, 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 of 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

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

So, in this case, you have

`\begin{gathered} (x_1,y_1)=(3,1) \\ (x_2,y_2)=(6,6) \end{gathered}`
`\begin{gathered} m=(6-1)/(6-3) \\ m=(5)/(3) \end{gathered}`

Now using the point-slope formula

`\begin{gathered} y-y_1=m(x-x_1) \\ y-1=(5)/(3)(x-3) \end{gathered}`

Therefore, the correct answer is D.

`y-1=(5)/(3)(x-3)`