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

Question

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

1. A. y = −x + 3 (Correct answer)
2. B. y = x − 3
3. C. y = −x − 3
4. D. y = x + 3

Correct Answer

Option A — y = −x + 3

Detailed Solution & Explanation

The correct answer is y = −x + 3.

Key Points

• Use the slope-intercept form, y = mx + c, where m is the slope and c the y-intercept.
• The slope is −1, so m = −1.
• The line passes through (0, 3), a point on the y-axis, so the y-intercept is c = 3.
• Substituting gives y = −x + 3.

Additional Information

• Any point of the form (0, k) is by definition the y-intercept, so no further substitution is needed — recognising that saves the whole calculation.
• Other forms of a straight line: point-slope y − y₁ = m(x − x₁), two-point form, and the general form ax + by + c = 0 with slope −a/b.
• Verify by substituting the point: at x = 0, y = −0 + 3 = 3 ✓. Testing the given point in each option is often the fastest route through these questions.

प्रश्न (हिन्दी में)

(0, 3) से होकर जाने वाली ढलान −1 वाली रेखा का समीकरण क्या है?

1. A. y = −x + 3
2. B. y = x − 3
3. C. y = −x − 3
4. D. y = x + 3