Question

Decide whether the lines are parallel, perpendicular or neither.

x + 4y = 7 and 4x – y = 3

Answer 1

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✔ x + 4y = 7

4y = - x +7

y = (-1/4) x + 7 

Slope of the equation x + 4y = 7 is -1/4.

Again, 4x – y = 3

y = 4x – 3

Slope of the equation 4x – y = 3 is 4.

Since multiplying both the slope of the equation = -1/4 × 4 = -1


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Answer 2

▶ The two equations are .

→ x + 4y = 7 ............(1) .

→ 4x - y = 3 ............(2) .

▶ Now, 

From equation (1) , 

°•° x + 4y = 7. 

==> 4y = 7 - x .

==> y = ¼( 7 - x ) .

•°• Therefore, the slope x + 4y = 7 is ¼ .

And,

From equation (2) ,

°•° 4x - y = 3 .

==> y = 4x - 3 .

•°• Therefore, the slope of 4x - y = 3 is 4 .

▶ From these two slopes , we find that 

→ The slope of 4x - y = 3 i.e., 4 is reciprocal of the slope of x + 4y = 7 i.e., ¼ . 

✔✔ Hence, the lines formed by these two equations is $\bf \underline{ \green { perpendicular }}$  ✅✅ .