# If given two points A(3, 12) and B(5, 22) on a x-y plane, find…

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## If given two points A(3, 12) and B(5, 22) on a x-y plane, find the equation of the straight line.

• A. y = 5x + 2
• B. y = 5x + 3
• C. y = 5x – 3
• D. y = 22x + 322

C

## DETAILS…

If two points on a straight line is given as (x₁ y₁), (x₂ y₂), then we will use the following equation to find the equation of the straight line

Cross multiplying, we have:

2(y – 12) = 10(x – 3)

2y – 24 = 10x – 30

Rearranging, we have:

2y = 10x – 30 + 24

2y = 10x – 6

Dividing through by 2, we have:

y = 5x – 3

### Now for the right answer to the above question:

1. Option A is incorrect.
2. Option B is incorrect.
3. C is correct.
4. D is not the correct answer.

## KEY-POINTS…

• You can also get this equation by using another formula which states: y = mx + c.
• Using the two given points to find the gradient(m), substituting it into y = mx + c, and using any of the two points to calculate c (the intercept on y axis).
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/ culled from 2019 JAMB-UTME mathematics question 21 /