What is the quation of line through (-1,-2) with slope -3.

Correct — A.
Point-slope form: y − y₁ = m(x − x₁), with (x₁, y₁) = (−1, −2) and m = −3
y − (−2) = −3(x − (−1))
y + 2 = −3(x + 1)

Expand the bracket: y + 2 = −3x − 3
Subtract 2: y = −3x − 5
Check: x = −1 gives y = 3 − 5 = −2, the given point → option (a)

Why the others are wrong

• (b)
  y = −3x + 1 — y = −3x + 1 is what (x − 1) in place of (x + 1) gives: y + 2 = −3(x − 1) = −3x + 3. This line passes through (1, −2), not (−1, −2).
• (c)
  y = −3x − 2 — −2 is the point's y-coordinate, not the y-intercept. This line crosses the y-axis at (0, −2), and at x = −1 it gives y = 3 − 2 = 1, missing (−1, −2).
• (d)
  y = −3x + 3 — At x = −1 this line gives y = 3 + 3 = 6, not −2. All four options share slope −3, so the intercept decides, and the point fixes it at −5.

A slope and one point fix a line. The point-slope form y − y₁ = m(x − x₁) builds it directly.

A second route is y = mx + c: substitute the point to find c. Here −2 = −3(−1) + c, so −2 = 3 + c and c = −5.

Every option has slope −3, so the task reduces to finding the intercept.

Key facts

• Point-slope form of a line: y − y₁ = m(x − x₁)
• In y = mx + c, m is the slope and c is the y-intercept
• A point lies on a line exactly when its coordinates satisfy the equation

Common traps

• Writing x − 1 for x − (−1), which leads to y = −3x + 1
• Taking the point's y-coordinate, −2, as the intercept

No directly related past PYQ was found.