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# The Equation of a Line 3x + 4y − 7 = 0. Find 1) the Slope of the Line. 2) the Equation of a Line Perpendicular to the Given Line and Passing Through the Intersection of the Lines X – Y + 2 = 0 and 3x + Y – 10 = 0. - ICSE Class 10 - Mathematics

#### Question

The equation of a line 3x + 4y − 7 = 0. Find

1) The slope of the line.

2) The equation of a line perpendicular to the given line and passing through the intersection of the lines x – y + 2 = 0 and 3x + y – 10 = 0.

#### Solution

3x + 4y – 7 = 0        .....(1)

1) Slope of the line m = "coefficient of x"/"coefficient of y" = -3/4

2) Equation of line perpendicular to the given line

4x – 3y = λ   ......(2)

Solving the equations x – y + 2 = 0 and 3x + y – 10 = 0, point of intersection is (2, 4).

Line (2) passes through points (2, 4).

4(2) – 3(4) = λ ⇒ λ  = –4

Hence, the equation of required line is

4x - 3y + 4 = 0

Is there an error in this question or solution?

#### APPEARS IN

2009-2010 (March) (with solutions)
Question 7.2 | 3.00 marks
Solution The Equation of a Line 3x + 4y − 7 = 0. Find 1) the Slope of the Line. 2) the Equation of a Line Perpendicular to the Given Line and Passing Through the Intersection of the Lines X – Y + 2 = 0 and 3x + Y – 10 = 0. Concept: Equation of a Line.
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