If (5, -2) is a point on the line PQ and the slope of the line PQ is 2, write the equation of the line PQ.
Hint: The formula of equation of line passing through a point and having a particular slope can be used to determine the solution. The equation of a line passing through a point (a, b) and having a slope m is given as: y-b = m(x-a).
Complete step-by-step answer: It is given that the line PQ passes through a particular point and has a particular slope.
We know that a line is represented uniquely if we know the slope of the line and a point it passes through. Hence, the line PQ can be uniquely represented by an equation.
The equation of a line passing through a point (a, b) and having a slope m is given as follows: \[y - b = m(x - a)............(1)\]
We know that the given line PQ passes through the point (5, -2) and has a slope of 2. Hence, the equation of line PQ using formula (1) is given as follows: \[y - ( - 2) = 2(x - 5)\]
Evaluating the brackets, we have: \[y + 2 = 2x - 10\]
Taking all the terms to one side, we have: \[2x - 10 - y - 2 = 0\]
Simplifying, we get: \[2x - y - 12 = 0\]
Hence, the equation of the line PQ is 2x – y – 12 =0.
Note: You might make a mistake in the slope-point formula of a line that passes through a point (a, b) and having slope m is given as y – a = m (x – b) which is wrong. The correct formula is y – b = m (x – a).
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