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Question
Line y = mx + c passes through the points A(2, 1) and B(3, 2). Determine m and c.
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Solution 1
Given, A(2, 1) and B(3, 2).
Equation of a line in two point form is
`(y - y_1)/(y_2 - y_1) = (x - x_1)/(x_2 - x_1)`
∴ the equation of the passing through A and B line is
`(y - 1)/(2 - 1) = (x - 2)/(3 - 2)`
∴ `(y - 1)/1 = (x - 2)/1`
∴ y – 1 = x – 2
∴ y = x – 1
Comparing this equation with y = mx + c, we get
m = 1 and c = – 1
Solution 2
Points A(2, 1) and B(3, 2) lie on the line y = mx + c.
∴ They must satisfy the equation.
∴ 2m + c = 1 ...(i)
and 3m + c = 2 ...(ii)
equation (ii) equation (i) gives m = 1
Substituting m = 1 in (i), we get
2(1) + c = 1
∴ c = 1 – 2 = – 1
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