Question

write an equation of a line that passes through (3,0) and (6,-3) in slope intercept and point slope form

Answer 1

The point-slope form:

`y-y_1=m(x-x_1)`

m - slope

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points (3, 0) and (6, -3). Substitute:

`m=(-3-0)/(6-3)=(-3)/(3)=-1`

The point-slope form:

`y-(-3)=-1(x-6)\\\\\boxed{y+3=-(x-6)}`

or

`y-0=-1(x-3)\\\\\boxed{y=-(x-3)}`

The slope-intercept form:

`y=mx+b`

m - slope

b - y-intercept

From the second point-slope form we have slope-intercept form:

`y=-(x-3)\\\\y=-x-(-3)\\\\\boxed{y=-x+3}`