Question

Write the equation of the line that passes through the points (7,9) and (9, -2). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answer 1

You have to find the equation of the line that passes through the points (7,9) and (9,-2)

To determine this equation you need to use the point-slope form:

$y-y_1=m(x-x_1)$

Where

m represents the slope of the line

(x₁,y₁) are the coordinates of one point of the line

Slope

As you can see, we need the slope of the line to determine its equation. To calculate the slope you have to use the following formula:

$m=\frac{y_1-y_2}{x_1-x_2}$

Where

(x₁,y₁) are the coordinates of one of the points of the line

(x₂,y₂) are the coordinates of the second point of the line

Using

(9,-2) as (x₁,y₁)

(7,9) as (x₂,y₂)

You can determine the slope of the line as follows:

$\begin{gathered} m=\frac{(-2)-9}{9-7} \\ m=-\frac{11}{2} \end{gathered}$

The slope of the line is m=-11/2

Equation:

Replace the slope and the coordinates of one of the point