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

Answer:

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:

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

Step-by-step 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:

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

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