Complete the equation of the line through (2,1) and (5,-8) use exact numbers

Answer 1

To find the equation of a line through two points, we need to find the slope and then use the point-slope form of a line.

Given the points (2, 1) and (5, -8), let's find the slope first.

The slope (m) can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁)

Using the coordinates (2, 1) as (x₁, y₁) and (5, -8) as (x₂, y₂), we have:
m = (-8 - 1) / (5 - 2)
m = -9 / 3
m = -3

Now, we can use the point-slope form of a line to get the equation.

The point-slope form of a line is:
y - y₁ = m(x - x₁)

Taking (2, 1) as (x₁, y₁) and substituting the slope (-3) and the coordinates of the point, we get:
y - 1 = -3(x - 2)

Now, let's multiply through to obtain the standard form of the equation:
y - 1 = -3x + 6

Finally, rearranging the equation into the standard form:
3x + y = 7

Thus, the equation of the line passing through (2, 1) and (5, -8) using exact numbers is 3x + y = 7.