Find an equation of the line having the given slope and containing the given point.
m = five sixths, (9, -2)
To find the equation of the line, we can use the point-slope form.
The point-slope form is given by: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Plugging in the values m = 5/6 and the coordinates (9, -2) into the equation, we have:
y - (-2) = (5/6)(x - 9)
Simplifying, we get:
y + 2 = (5/6)(x - 9)
Multiplying both sides by 6 to eliminate the fraction, we get:
6(y + 2) = 5(x - 9)
Expanding the equation, we have:
6y + 12 = 5x - 45
Rearranging the equation to the standard form, we get:
5x - 6y = 57
Therefore, the equation of the line with slope 5/6 and passing through the point (9, -2) is 5x - 6y = 57.