Find the equation of the line through the points (-2, 1) and (-$\frac{1}{2}$, 4)

Analyze the question: We need the equation of a straight line passing through two given points, (-2, 1) and (-1/2, 4).

Concept: A straight line has the form y = mx + c, where m is the gradient and c is the y-intercept. The gradient between two points is

m = (y₂ − y₁) / (x₂ − x₁)

Step 1: Find the gradient

m = (4 − 1) / (−1/2 − (−2)) m = 3 / (−1/2 + 2) m = 3 / (3/2) m = 2

Step 2: Find c using the point (−2, 1)

y = 2x + c 1 = 2(−2) + c 1 = −4 + c c = 5

So the equation is y = 2x + 5.

Step 3: Check with the second point (−1/2, 4)

y = 2(−1/2) + 5 = −1 + 5 = 4 ✓

Check the options:

• A. y = 2x − 3: at x = −2, y = −7, which is not 1 ✗
• B. y = 2x + 5: at x = −2, y = 1 ✓, and at x = −1/2, y = 4 ✓
• C. y = 3x − 2: at x = −2, y = −8 ✗
• D. y = 2x + 1: at x = −2, y = −3 ✗

Exam tip: When the options are equations of lines, substitute one of the given points into each option. Only the correct line will satisfy both points, and this can save you time in JAMB. Also, be careful when subtracting negative numbers, such as −1/2 − (−2), because this is where most mistakes happen.