Question

How do you write an equation in point slope and slope intercept form parallel to y=1/2x-1 point: (0,-4)?

Answer 1

`y+4=1/2(x-0)`

Explanation:

Point slope form is `y-color(blue)(y_1)=color(magenta)m(x-color(red)(x_1))`
where `color(magenta)m=` slope and `(color(red)(x_1),color(blue)(y_1))` is a point.

Parallel lines have the same slope. The equation
`y=color(magenta)(1/2)x-1` is in the form `y=color(magenta)mx+b` where `color(magenta)m=`slope.

The slope in this example is `color(magenta)(1/2)`, and the parallel slope is also `color(magenta)(1/2)`.

The point `(color(red)(x_1),color(blue)(y_1))` is `(color(red)0,color(blue)(-4))`.

So the equation in point slope form is

`y-color(blue)(-4)=color(magenta)(1/2)(x-color(red)0)`

`y+4=1/2(x-0)`