Question

The slope-intercept form of the equation of a line that passes through point (–3, 8) is y = –2/3x + 6. What is the point-slope form of the equation for this line?

Answer 1

To help you out, the equation for point slope form is y-y1 = m(x-x1)

You just plug the numbers in and solve. :)

y-8=-2/3(x+3)
y-8=-2/3x -2
y= -2/3x -2 -8
y=-2/3x - 10 is your answer.

Answer 2

The point slope form of the line is
`y-8=-(2)/(3)(x+3)`.

Explanation:

The slope intercept form of a line is

`y=mx+b` .... (1)

where, m is slope and b is y-intercept.

The given equation is

`y=-(2)/(3)x+6` .... (2)

From (1) and (2) it is clear that

`m=-(2)/(3),b=6`

The slope of the line is
`-(2)/(3)`.

The point slope form of a line is

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

Where, m is slope.

The slope of the line is
`-(2)/(3)` and it passes through the point (-3,8).

`y-8=-(2)/(3)(x-(-3))`

`y-8=-(2)/(3)(x+3)`

Therefore the point slope form of the line is
`y-8=-(2)/(3)(x+3)`.