What is the equation of line through (0,3) with slope −1?

Correct — A. The point (0, 3) lies on the y-axis, so it is the y-intercept.

Slope-intercept form: y = mx + c
Slope m = −1, intercept c = 3
Substitute: y = (−1)x + 3
y = −x + 3 → option (a)

Why the others are wrong

• (b)
  y = x − 3 — y = x − 3 has slope +1 and crosses the y-axis at (0, −3). Both the slope and the intercept carry the wrong sign.
• (c)
  y = −x − 3 — y = −x − 3 has the right slope, −1, but at x = 0 it gives y = −3. The line must pass through (0, 3).
• (d)
  y = x + 3 — y = x + 3 does pass through (0, 3), but its slope is +1. It rises to the right, while a slope of −1 falls.

A straight line is fixed by one point and its slope. In y = mx + c, m is the slope and c is where the line meets the y-axis, at (0, c).

For a point off the y-axis, use point-slope form, y − y₁ = m(x − x₁). With (0, 3) and m = −1 it gives y − 3 = −x, the same line.

Key facts

• Slope-intercept form: y = mx + c, with slope m and y-intercept c.
• Point-slope form: y − y₁ = m(x − x₁).
• A negative slope means y falls as x increases.
• (0, 3) satisfies y = −x + 3 and y = x + 3, but not y = x − 3 or y = −x − 3.

Common traps

• Checking only the point: y = x + 3 also passes through (0, 3), so the slope has to be checked too
• Dropping the minus sign of the slope

No directly related past PYQ was found.