Question

A line intersects the point (-11,4)and has a slope of -2. What are the inputs to the point -slope formula?

Answer 1

The inputs to this formula are:

• The x-coordinate of the point:
  `x_0 = -11`;
• The y-coordinate of the point:
  `y_0 = 4`; and
• The slope of the line:
  `m = -2`.

The equation of this line in point-slope form will be:

`y - 4 = -2(x +11)`.

Explanation:

The general form of a 2D line in its point-slope form is:

`l:\; y - y_0 = m(x - x_0)`.

This form of the equation of a line takes two pieces of information:

• The x-y coordinate of a point on the line
  `(x_0, y_0)`, and
• The slope (a.k.a. gradient) of that line.

For this line, the point
`(x_0, y_0)` is
`(-11, 4)`.

• 
  `x_0 = -11`, and
• 
  `y_0 = 4`.

The slope of this line is
`-2`. In other words,

• 
  `m = -2`.

Apply the point-slope formula for a 2D line:

`l:\; y - 4 = -2 (x - (-11))`.

`l:\; y - 4 = -2 (x +11 )`.