Answer: The correct answer is D.
Explanation:
To find the equation of the line passing through the points (2, 5) and (1, 3), we can use the point-slope form of the equation of a line:
y - y₁ = m(x - x₁)
where (x₁, y₁) are the coordinates of one of the points on the line, and m is the slope of the line.
Let's use the first point (2, 5):
y - 5 = m(x - 2)
Now, we need to find the slope (m) using the second point (1, 3):
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - 5) / (1 - 2)
m = -2 / -1
m = 2
Now that we have the slope (m = 2), we can substitute it into the equation with the coordinates of the first point (2, 5):
y - 5 = 2(x - 2)
Next, distribute the 2 on the right side:
y - 5 = 2x - 4
To isolate y, add 5 to both sides:
y = 2x - 4 + 5
Simplify:
y = 2x + 1
So, the equation that represents the line passing through the points (2, 5) and (1, 3) is:
y = 2x + 1