Question

given pt m(8,4) & pt N (5,2) find the equation of line m-n

Answer 1

Find the slope, then then construct your line equation. I prefer\[y=mx+b\]where m is the slope and b is the y-intercept.

Answer 2

so the slope is -2/3?

Answer 3

and b=4

Answer 4

\[m=\frac{\Delta y}{\Delta x}=\frac{2}{3}\]
The slope is not negative, because as your x increases (+), your y increases (+).

Answer 5

\[y=\frac{2}{3}x+b\]Take a given point (x,y) and substitute it back into the line equation for x and y, this allows you to solve for b.

Answer 6

2=2/3(5)?

Answer 7

I am going to use point (5,2) to find b.\[y=\frac{2}{3}x+b\]\[b=y-\frac{2}{3}x\]\[b=(2)-\frac{2}{3}(5)\]\[b=2-\frac{10}{3}=\frac{6}{3}-\frac{10}{3}\]\[b=-\frac{4}{3}\]

Answer 8

\[y=\frac{2}{3}x-\frac{4}{3}\]Test using point m(8,4)\[(4)=\frac{2}{3}(8)-\frac{4}{3}\]\[4=\frac{12}{3}\]\[4=4\]It checks out.