Question

the coordinate plane above, there is a circle with center at point (4,3 A(1,-1) and B(8,6). Determine the equation of the line that goes through points A and Does this line pass through the center of the circle? Explain how you

Answer 1

we have 2 points, A(1,-1) and B(8,6). We have to calculate the slope

$m=\frac{6-(-1)}{8-1}=\frac{7}{7}=1$

so we have that the equation is

$\begin{gathered} y-6=x-8 \\ y=x-8+6=x-2 \end{gathered}$

so we get that first asnwer is:

$y=x-2$

TO know if it pass through the center, we have to replace y by 4 and x by 3

$\begin{gathered} 4=3-2=1\rightarrow4=1,\text{ but} \\ 4\ne1 \end{gathered}$

so the answer for the second question is no. when you replace y by 4 and x by 3 you get something that is a lie, so that point does not belong to the line.