Question

What is the equation in point-slope form and slope intercept form for the line given slope= 8/3,(-2,-6)?

Answer 1

General point slope form :
`y-y_1 = m(x-x_1)`
for a given slope `m` and a point on the line `(x_1,y_1)`

From the given data:
`y+6 = 8/3(x+2)`

General slope-intercept form:
`y=mx+b`
for a given slope `m` and a y-intercept `b`

From the given data
`y = 8/3x+b`
but we still need to determine the value of `b`
If we insert the values of the point `(x,y) = (-2,-6)`
`-6 = 8/3(-2)+b`
`b= -6 +16/3 = -6 +5 1/3 = -2/3`
and the slope-intercept form is
`y= 8/3x -2/3`