Answer:
y + 5 = 3(x + 1) → point-slope form
y = 3x - 2 → slope-intercept form
3x - y = 2 → standard form
Explanation:
The point-slope form of an equation of a line:
y - y₁ = m(x - x₁)
m - a slope
(x₁, y₁) - a point on a line
We have
m = 3, (-1, -5) → x₁ = -1, y₁ = -5
Substitute:
y - (-5) = 3(x - (-1))
y + 5 = 3(x + 1) → point-slope form
convert to the slope-intercept form y = mx + b:
y + 5 = 3(x + 1) use the distributive property: a(b + c) = ab + ac
y + 5 = 3x + 3 subtract 5 from both sides
y = 3x - 2 → slope-intercept form
convert to the standard form Ax + By = C:
y = 3x - 2 subtract 3x from both sides
-3x + y = -2 change the signs
3x - y = 2 → standard form