Question

Decide whether the lines are parallel, perpendicular or neither.

x + 4y = 7 and 4x – y = 3
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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

Therefore, the given two equations are perpendicular to each other.

Answer: Perpendicular

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 .

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

prependicular