Question

Now, find the equation for a line that passes through the two points (−1,3) and (4,−5).

Answer 1

First find slope(m):
y1-y2 -5-3 -8 -8
------- = -------- = ------ = ----
x1-x2 4-(-1) 4+1 5

m= -8/5

Then use intercept form:
y1-y2=m(x1-x2)

Plug in slope and one of the given points:
y-3= -8/5(x-(-1))
y-3= -8/5(x+1)
y-3= (-8/5)x-8/5
y= (-8/5)x+7/5

Answer:
y=(-8/5)x+7/5

Check:

y=(-8/5)(-1)+7/5
y=8/5+7/5
y= 15/5
y=3
yes

y=(-8/5)(4)+7/5
y= -32/5 + 7/5
y= -25/5
y= -5
yes