Question

How do you write the point slope form of the equation given (-4,1) parallel to `y=-1/2x-1`?

Answer 1

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

Explanation:

The equation of a line in `color(blue)"point-slope form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1)" a point on the line"`

`"require to know the following fact."`

`color(red)(bar(ul(|color(white)(2/2)color(black)(" parallel lines have equal slopes")color(white)(2/2)|)))`

`y=-1/2x-1" is in slope-intercept form, that is"`

`y=mx+brArr" slope " = m=-1/2`

`"using " m=-1/2" and " (x_1,y_1)=(-4,1)`

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

`rArry-1=-1/2(x+4)larrcolor(red)" in point-slope form"`