complete the equation og the line throught (2,1) and (5,-8)

Answer 1

To find the equation of the line through the points (2,1) and (5,-8), we can first find the slope of the line using the formula:

slope = (change in y) / (change in x)

Let's label the coordinates of the first point as (x₁, y₁) and the second point as (x₂, y₂). Using the formula above, we have:

slope = (y₂ - y₁) / (x₂ - x₁)
slope = (-8 - 1) / (5 - 2)
slope = -9 / 3
slope = -3

Now that we have the slope of the line, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by:

y - y₁ = m(x - x₁)

Using the coordinates (2,1), we have:

y - 1 = -3(x - 2)

Expanding and rearranging the equation, we get:

y - 1 = -3x + 6
y = -3x + 7

Therefore, the equation of the line through (2,1) and (5,-8) is y = -3x + 7.