The first step of writing an equation when given two points is the same for both strategies, slope-intercept or point-slope forms. What would be the first step in finding the equation of the line that passes through (5, 1) and (3, 5)?

Question

create a graph using the two points
find the slope
find the y-intercept
substitute one point’s coordinates into either form

Answer 1

The first step in finding the equation of the line that passes through the points (5, 1) and (3, 5) is to find the slope.

The slope \( m \) can be calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, we can assign the points as follows:

• Point 1: \( (x_1, y_1) = (5, 1) \)
• Point 2: \( (x_2, y_2) = (3, 5) \)

Plugging in these values:

\[ m = \frac{5 - 1}{3 - 5} = \frac{4}{-2} = -2 \]

So, the first step is indeed to find the slope. After that, you can proceed with either the slope-intercept form or the point-slope form to find the equation of the line.