Question

Question #a22d8

Answer 1

`C: y-4=1/6(x+5)`

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"`

`"here "m=1/6" and "(x_1,y_1)=(-5,4)`

Substitute these values into the equation.

`y-4=1/6(x-(-5))`

`rArry-4=1/6(x+5)larrcolor(red)" in point-slope form"`

We can distribute the bracket and simplify to obtain another version of the equation.

`y-4=1/6x+5/6`

`y=1/6x+5/6+4`

`rArry=1/6x+29/6larrcolor(red)" in slope-intercept form"`