Question

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

Answer 1

The point-slope form:

`y - y_1 = m\;(x - x_1)`.

The inputs are:

• 
  `y_1 = -2`,
• 
  `x_1= -11`, and
• 
  `m = -2`.

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

`y {\bf + 2} = {\bf -2} \;(x {\bf+11})`.

Explanation:

Why the point-slope form?

Prefer this form in case both of the following are given:

• The coordinates of a point on the line, and
• The slope (a.k.a. gradient) of the line.

What is the equation of a line in the point-slope form?

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

where
`x` and
`y` are variables. The point-slope form takes three parameters:

• 
  `x_1`, the x-coordinate of the given point;
• 
  `y_1`, the y-coordinate of the given point; and
• 
  `m` the slope of the line.

The coordinate of the given point on the line is

`(\underbrace{-11}_(x_1), \underbrace{-2}_(y_1))`.

In other words,

• 
  `x_1 = -11`, and
• 
  `y_1 = -2`.

The slope of the line is -2. As a result,

• 
  `m = -2`.

Hence the equation:

`y - (-2) = -2\;(x - (-11))`

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