# 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.

Last updated date: 21st Mar 2023

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Answer

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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).

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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