Question

help writing an equation where the line passes through the given points (10, -5), (-5,1)???

Answer 1

I am assuming you are using the slope-intercept form \[y=mx+b\] where the \[m\] is the slope and the \[b\] is the y-intercept. First you will have to use your two points to find the slope.

\[m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-5)}{-5-10}=\frac{6}{-15}=-\frac{2}{5}\]. From here, we can substitute this into your slope-intercept equation for m. This gives \[y=-\frac{2}{5}x+b\]. Now, substitute an x-value and a y-value from one of your points to find the value of b.

If you use the point \[(10,-5)\] you will have \[-5=-\frac{2}{5} \cdot 10 + b\]. Simplifying and solving you get
\[-5=-4+b\]
\[-1=b\].

Thus, you have \[m=-\frac{2}{5}\] and \[b=-1\] which gives you the equation \[y=-\frac{2}{5}x-1\]

Answer 2

cmorss, props for having one of the most beautiful answers to algebra that I've ever seen.