Question

30 POINTS. Given ABC with coordinates A(-6,1), B(4,1), and C(4,-3). the ordered pair (9,y) is on the line ac. Enter the value of y for this ordered pair.

Answer 1

The value of y is -5, so the ordered pair is (9, -5).

Explanation:

To determine the value of y for the ordered pair (9, y) on the line AC, we first need to find the equation of the line AC.

To find the slope of the line AC, substitute the points A and C into the slope formula:

`\textsf{Slope}\;(m)=(y_2-y_1)/(x_2-x_1)=(y_C-y_A)/(x_C-x_A)=(-3-1)/(4-(-6))=(-4)/(10)=-(2)/(5)`

To determine the equation of line AC, substitute the found slope and one of the points into the point-slope formula:

`\begin{aligned}y-y_1&=m(x-x_1)\\\\y-1&=-(2)/(5)(x-(-6)\\\\y-1&=-(2)/(5)x-(12)/(5)\\\\y&=-(2)/(5)x-(7)/(5) \end{aligned}`

Now we have found the equation of the line AC, to determine the value of y for the ordered pair (9, y), substitute x = 9 into the equation:

`\begin{aligned}y&=-(2)/(5)(9)-(7)/(5)\\\\&=-(18)/(5)-(7)/(5)\\\\&=(-18-7)/(5)\\\\&=(-25)/(5)\\\\&=-5\end{aligned}`

Therefore, the value of y for the ordered pair is y = -5.

So the ordered pair is (9, -5).