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