Find y if the point (-6,y) is on the line that passes through (-1,-7) and (3,-2).
There are a few ways to approach this question. Here was my approach.
A point lies on an arbitrary line if the slope between any two points always remains constant. We already have two points, so we can determine the slope of this arbitrary line in space. Be careful with your signs!
\(m=\frac{\text{change in y}}{\text{change in x}}\\ m=\frac{-2-(-7)}{3-(-1)}\\ m=\frac{5}{4}\)
Now, let's find the slope between \((-6,y)\text{ and }(-1,-7)\).
\(m=\frac{\text{change in y}}{\text{change in x}}\\ m=\frac{y-(-7)}{-6-(-1)}\\ m=\frac{y+7}{-5}\\ \)
As I already stated, the slopes must be the same in order for this point to be on this line. It is now possible to solve for y.
\(\frac{y+7}{-5}=\frac{5}{4}\\ 4(y+7)=-5*5\\ 4y+28=-25\\ 4y=-53\\ y=-\frac{53}{4}\)
There are a few ways to approach this question. Here was my approach.
A point lies on an arbitrary line if the slope between any two points always remains constant. We already have two points, so we can determine the slope of this arbitrary line in space. Be careful with your signs!
\(m=\frac{\text{change in y}}{\text{change in x}}\\ m=\frac{-2-(-7)}{3-(-1)}\\ m=\frac{5}{4}\)
Now, let's find the slope between \((-6,y)\text{ and }(-1,-7)\).
\(m=\frac{\text{change in y}}{\text{change in x}}\\ m=\frac{y-(-7)}{-6-(-1)}\\ m=\frac{y+7}{-5}\\ \)
As I already stated, the slopes must be the same in order for this point to be on this line. It is now possible to solve for y.
\(\frac{y+7}{-5}=\frac{5}{4}\\ 4(y+7)=-5*5\\ 4y+28=-25\\ 4y=-53\\ y=-\frac{53}{4}\)
