Question

Match slope field with the equation(see attached photo) How do you do this?

Answer 1

lats do the easiest first to see how to do these :

7. \(y = 1\) matches with graph \(D\)

Answer 2

how do you know?

Answer 3

\(y = 1\)

\(y' = 0\)

the slope at everypoint on solutions curves is 0

Answer 4

heard of the term "isocline" before ?

Answer 5

if not,
slope = 0 are just the horizontal lines,
the slope field that closely matches with horizontal lines is graph D

Answer 6

ok

Answer 7

how do we do the others?

Answer 8

on the same veins, lets do one more :
8. \(y = x\) matches with graph \(H\)

Answer 9

how?

Answer 10

find the slope :

\(y′=1\)

the slope at every point on solution curve is 1,
look at the given graphs and see which graph has constant slope "dashes" everywhere

Answer 11

you will find that graph \(H\) has dashes with fixed slope of 1 everywhere