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

Answer:

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:

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

Step-by-step 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:

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

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