Question

Through the origin and (-5,4) point slope form, step by step.

Answer 1

For this case we have that by definition, the point-slope equation is given by:

`(y-y_ {0}) = m (x-x_ {0})`

Where:

m: It's the slope
`m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}\\(x_ {1}, y_ {1}) :( 0,0)\\(x_ {2}, y_ {2}): (- 5,4)`

Substituting:

`m = \frac {4-0} {- 5-0} = - \frac {4} {5}`

Thus, the equation is of the form:

`(y-y_ {0}) = - \frac {4} {5} (x-x_ {0})`

We substitute a point:
`(y-0) = - \frac {4} {5} (x-0)\\y = - \frac {4} {5} x`

Answer:

`y = - \frac {4} {5} x`