Question

A line with slope - passes through point Q (6, 7). Does point S (2,5) lie on the same line? Without graphing, explain how you found youranswer.

Answer 1

Let:

(x1,y1) = (6,7)

m = -1/2

Using the point-slope equation:

`\begin{gathered} y-y1=m(x-x1) \\ y-7=-(1)/(2)(x-6) \\ y-7=-(1)/(2)x+3 \\ y(x)=-(1)/(2)x+10 \end{gathered}`

The point S(2,5) lie on the same line if the point satisfies the equation, so:

`\begin{gathered} S(2,5) \\ x=2,y=5 \\ y(2)=5 \\ 5=-(1)/(2)(2)+10 \\ 5=-1+10 \\ 5=9 \\ \text{This is false, because} \\ 5\\e9 \end{gathered}`

Since the point doesn't satisfy the equation, we can conclude that the point S(2,5) is not on the same line