Question

Determine another point on the line given two points on the line. (-2, 9), (2, -1)

Answer 1

Answer:

(4,-6)  

Step-by-step explanation:

1) First, let's find the slope of the line between the two points. Use the slope formula $m = \frac{y_2-y_1}{x_2-x_1}$, substitute the x and y values of (-2,9) and (2,-1) into it, then solve:

$m = \frac{(-1)-(9)}{(2)-(-2)}\\m = \frac{-1-9}{2+2} \\m =\frac{-10}{4} \\m = -\frac{5}{2}$

So, the slope of the line is $-\frac{5}{2}$.

2) Now, using that slope, let's find another point on the line. You can do this by drawing the two points on a graph (picture below). Now, remember that the slope is $\frac{rise}{run}$. So, starting from any of the two points (I chose (2,-1), as seen below) count 5 units down, then 2 units to the right. This gives an answer, (4,-6).