Question

2:Here are four straight line equations.
A.3y=4x+5
B.4y=3x-1
C.4y+3x=7
D.4x+3y=2
Which one of the following statements is true? Explain by working
A. Lines 1 and 2 are perpendicular
B. Lines 1 and 4 are parallel
C. Lines 2 and 4 are perpendicular
D. Lines 2 and 3 are parallel
E. I don't know

Answer 1

Answer:

C. Lines 2 and 4 are perpendicular

Step-by-step explanation:

1. 3y = 4x + 5  => y = 4/3x + 5/3

2. 4y = 3x - 1   => y = 3/4x - 1/4

3. 4y + 3x = 7   => 4y = -3x + 7  => y = -3/4x + 7/4

4. 4x + 3y = 2  => 3y = -4x + 2 => y = -4/3x + 2/3

Comparing the above equations with y = mx+c,

we find that the

Slope of 1 (m1) = 4/3

Slope of 2 (m2) = 3/4

Slope of 3 (m3) = -3/4

Slope of 4 (m4) = -4/3.

We see that None of the slopes are equal to each other.

So, no lines are parellel.

Also, we see that m1*m3 = 4/3*-3/4 = -1

                             m2*m4 = 3/4*-4/3 = -1

We know, that the product of slopes of perpendicular lines = -1

Hence, lines 1 and 3 are perpendicular and lines 2 and 4 are perpendicular.

Note :- Opt. E. can also be justified as correct if it is true. :)