Answer:
y - 12 = 5(x - 3) {the point-slope form of the equation}
y = 5x + 9 {the slope-intercept form of the equation}
5x - y = -9 {standard form of the equation}
Step-by-step explanation:
The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:
y = 5x - 7 ⇒ m = 5
(3, 12) ⇒ x₀ = 3, y₀ = 12
So, the point-slope form of the equation:
y - 12 = 5(x - 3)
Therefore:
y - 12 = 5x - 3 {add 12 to both sides}
y = 5x + 9 ← the slope-intercept form of the equation
y = 5x + 9 {subtract5x from both sides}
y - 5x = 9 {multiply both sides by (-1)}
5x - y = -9 ← the standard form of the equation
