Question

What is the point-slope form of a line that has a slope of –4 and passes through point (–3, 1)?

Answer 1

y - 1 = - 4(x + 3)

Explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 4 and (a, b) = (- 3, 1), hence

y - 1 = - 4(x - (- 3)), thus

y - 1 = - 4(x + 3) ← in point- slope form

Answer 2

`y-1=-4(x+3)`

Explanation:

Given: A line has a slope of -4 and the line passes through a point
`(-3, 1)`.

To find: The point-slope form of this line.

Solution:

We know, the point-slope form of a line can be given as

`y-y_(1)=m(x-x_(1) )`

Here,
`m` is the slope of the line, and
`(x_(1), y_(1))` is the point through which it passes.

The slope of the line is -4, and the point is
`(-3, 1)`.

So,
`m=-4`,
`x_(1) =-3`, and
`y_(1) =1`.

Now, putting the values in the equation, we get

`y-1=-4(x-(-3))`

`y-1=-4(x+3)`

Therefore, the point-slope form of the line is
`y-1=-4(x+3)`.