Answer:
y + 2 = ⁶/₅(x - 5) {the point-slope form of the equation}
y = ⁶/₅x - 8 {the slope-intercept form of the equation}
6x - 5y = 40 {the standard form of the equation}
Explanation:
The point-slope form of equation is: y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope.
m = ⁶/₅
(5, -2) ⇒ x₀ = 5, y₀ = -2
So, the point-slope form of the equation:
y + 2 = ⁶/₅(x - 5)
Therefore:
y + 2 = ⁶/₅x - 6 {subtract 2 from both sides}
y = ⁶/₅x - 8 ← the slope-intercept form of the equation
-⁶/₅x + y = - 8 {multiply both sides by (-5)}
6x - 5y = 40 ← the standard form of the equation