Which equation represents the line that passes through the points (4, 1) and (0, 3)?
To determine the equation of a line passing through two points, we can use the point-slope form.
The slope of the line can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Let's substitute the values given:
m = (3 - 1) / (0 - 4)
m = 2 / -4
m = -1/2
Now we can choose either of the two points and the slope obtained to write the equation of the line using the point-slope form:
y - y₁ = m(x - x₁)
Let's choose the point (4, 1):
y - 1 = (-1/2)(x - 4)
Distributing -1/2 on the right side:
y - 1 = (-1/2)x + 2
Adding 1 to both sides:
y = (-1/2)x + 3
Therefore, the equation of the line that passes through the points (4, 1) and (0, 3) is y = (-1/2)x + 3.