Question

How do you write the point slope form of the equation given (0,-2) and (-1,2)?

Answer 1

`y+2=-4(x-0)`

Explanation:

Begin with finding the slope by using the slope formula: `m=(y_2-y_1)/(x_2-x_1)`

If we let `(color(red)0,color(blue)(-2))->(color(red)(x_1),color(blue)(y_1))` and `(color(red)(-1),color(blue)(2))->(color(red)(x_2),color(blue)(y_2))` then,

`m=color(blue)(2-(-2))/(color(red)(-1-0))=4/-1=-4`

Using the slope and any of the two points above, we can determine the slope of the line in point-slope form by using this formula: `y-y_1=m(x-x_1)`. I will use the point `(0,-2)`

If we let `m=-4` and `(color(red)0,color(blue)(-2))->(color(red)(x_1),color(blue)(y_1))` then:

`y-color(blue)((-2))=-4(x-color(red)0)`

`y+2=-4(x-0)`