What is the equation of the line that passes through the points (4, 1) and (2, 3)?

Finding the Equation of a Line

To determine the equation of the line that passes through the points (4, 1) and (2, 3), we can follow these steps:

Step 1: Calculate the Slope

The first step is to find the slope (m) of the line using the formula:

m = (y2 - y1) / (x2 - x1)

Here,

• (x₁, y₁) = (4, 1)
• (x₂, y₂) = (2, 3)

Substituting the values:

m = (3 - 1) / (2 - 4) = 2 / -2 = -1

Step 2: Use the Point-Slope Form of the Equation

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

Substituting one of the points, say (4, 1), and the slope (-1):

y - 1 = -1(x - 4)

Step 3: Simplify the Equation

Now, let’s simplify the equation:

y - 1 = -x + 4

Adding 1 to both sides gives us:

y = -x + 5

Final Equation

Thus, the equation of the line that passes through the points (4, 1) and (2, 3) is:

y = -x + 5

This means the line has a slope of -1 and crosses the y-axis at 5.