Question

find another ordered pair(coordinate) that falls on the line that passes through (-5,2) and (1, -2).

Explanation:

Step1: Find the slope

First, we use the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \) with the points \((-5, 2)\) and \((1, -2)\). Let \((x_1, y_1)=(-5, 2)\) and \((x_2, y_2)=(1, -2)\). Then \( m=\frac{-2 - 2}{1 - (-5)}=\frac{-4}{6}=-\frac{2}{3} \).

Step2: Use the slope - intercept form

The slope - intercept form of a line is \( y=mx + b \). We can use one of the points to find \( b \). Let's use the point \((1, -2)\). Substitute \( x = 1 \), \( y=-2 \) and \( m =-\frac{2}{3} \) into \( y=mx + b \):
\(-2=-\frac{2}{3}(1)+b\)
\(-2=-\frac{2}{3}+b\)
Add \(\frac{2}{3}\) to both sides: \( b=-2+\frac{2}{3}=\frac{-6 + 2}{3}=-\frac{4}{3} \)
So the equation of the line is \( y =-\frac{2}{3}x-\frac{4}{3} \).

Step3: Find another point

We can choose a value for \( x \) and find the corresponding \( y \). Let's choose \( x = 4 \). Then \( y=-\frac{2}{3}(4)-\frac{4}{3}=-\frac{8}{3}-\frac{4}{3}=-\frac{12}{3}=-4 \). So the point \((4, -4)\) lies on the line. (We can also choose other values of \( x \), for example, if \( x = 7 \), \( y=-\frac{2}{3}(7)-\frac{4}{3}=-\frac{14 + 4}{3}=-6 \), so \((7, -6)\) is also on the line)

Answer:

One possible ordered pair is \((4, - 4)\) (or other pairs like \((7, -6)\), \((-2,0)\) etc. can also be correct as long as they satisfy the line equation \( y=-\frac{2}{3}x-\frac{4}{3} \))