Write the equation of the linear function that passes through the points (2, -2) and ( 6,0). Help Video, if needed.

Answer 1

To find the equation of the linear function that passes through the points (2, -2) and (6, 0), we first need to find the slope of the line.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)

Substitute the values of the points into the formula:
m = (0 - (-2)) / (6 - 2)
m = 2 / 4
m = 1/2

Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y₁ = m(x - x₁)

Substitute the slope and one of the points into the equation:
y - (-2) = (1/2)(x - 2)
y + 2 = (1/2)(x - 2)

Now we can simplify the equation:
y + 2 = (1/2)x - 1
y = (1/2)x - 3

Therefore, the equation of the linear function that passes through the points (2, -2) and (6, 0) is y = (1/2)x - 3.