Find the equation of a line which is form origin and passes through the point (−3, −4)

Analyze the question: The line starts from the origin (0, 0) and passes through (−3, −4). We need its equation.

Concept: A line through the origin has the form y = mx, where m is the gradient. The gradient between two points is

m = (y₂ − y₁)/(x₂ − x₁)

Solution:

1. Use the points (0, 0) and (−3, −4):

m = (−4 − 0)/(−3 − 0) = (−4)/(−3) = 4/3

2. Substitute into y = mx:

y = 4x/3

Check: Put x = −3 into y = 4x/3: y = 4(−3)/3 = −4 ✓. This matches the point (−3, −4).

The other options fail the check. For example, option A gives y = 3(−3)/4 = −9/4, which is not −4.

Tip: For a line through the origin, the equation is always y = (y/x)x using the given point. Just divide y by x to get the gradient. Here, −4 ÷ −3 = 4/3. Remember that two negatives make a positive.