Find the value of c such that the three points (5,5), (3,1), and (-6,c) lie on the same line.
Note: Three points are on the same line if the slope of the line through any two points is always the same.
+2668 Solution 1:
The slope between \((5,5)\) and \((3,1)\) is \({{1-5} \over {3-5} } = 2\)
To get from x coordinate \(3\) to x coordinate \(-6 \), you need to subtract \(9\), meaning that the y-value would be \(18\) less than \(1\), s \(c = \color {red} -17 \).
Solution 2:
Using the method above, you know that the slope is -2, so when you plug it into the equation \(y=mx+b\), with \(x = 5\), \(y = 5\), and \(m= 5 \) (coordinates of 1 point doesn't matter which, and slope respectively), you get: \(5 = 2 \times 5 + b\), where \(b = -5\), giving us the equation \(y=2x-5\).
Plug in \(x = -6\), and you find that \(c = \color{Red} 17\)
