What is an equation for the line that passes through the points (–2, 3) and (2, 1)?

To find the equation of the line that passes through the points (-2, 3) and (2, 1), we need to follow these steps:

Step 1: Find the slope (m) of the line. The formula to find the slope when given two points (x1, y1) and (x2, y2) is:

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

Substituting the given points (-2, 3) and (2, 1) into the formula, we get:

m = (1 - 3) / (2 - (-2)) = -2 / 4 = -0.5

Step 2: Use the point-slope form of a line equation to find the equation of the line. The point-slope form of a line equation is:

y - y1 = m(x - x1)

We can use either of the given points for (x1, y1). Let's use (-2, 3):

y - 3 = -0.5(x - (-2))

Simplify the equation:

y - 3 = -0.5x - 1

Add 3 to both sides to solve for y:

y = -0.5x + 2

So, the equation of the line that passes through the points (-2, 3) and (2, 1) is y = -0.5x + 2.