Which equation represents the line that passes through the points (6, 3) and (4, 9)?

To find the equation of the line that passes through the points (6, 3) and (4, 9), we start by determining the slope of the line using the formula:

m = (y₂ – y₁) / (x₂ – x₁)

Here, we can let (x₁, y₁) be (6, 3) and (x₂, y₂) be (4, 9). Substituting the values:

m = (9 – 3) / (4 – 6) = 6 / -2 = -3

Now that we have the slope (m = -3), we can use the point-slope form of the equation of a line, which is given by:

y – y₁ = m(x – x₁)

Substituting (x₁, y₁) = (6, 3) and m = -3 into the equation:

y – 3 = -3(x – 6)

Expanding this gives us:

y – 3 = -3x + 18

Rearranging to put it in slope-intercept form (y = mx + b):

y = -3x + 21

Therefore, the equation of the line that passes through the points (6, 3) and (4, 9) is:

y = -3x + 21