Question

Decide whether the lines are parallel, perpendicular or neither.

x + 4y = 7 and 4x – y = 3​

Answer 1

Answer:

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Step-by-step explanation:

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

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Answer 2

Given

x + 4y = 7

x/7 + y/(7/4) = 1

so point p = (7,7/4)

x = 7 and y = 7/4

4x - y = 3 ----(1

LHS

4x - y

put value of x and y

28 - 7/4

(112 - 7)/4

105/4

since LHS not equal to RHS

so both line are not parallel

we know that

y = mx + C

Now

X + 4y = 7

y = 7/4 - x/4

m1 = -1/4

equation 2

4x - y = 3

y = 4x - 3

m2 = 4

for condition of perpendicular

M1*M2 = -1

LHS

-1*4/4

-1

Hence LHS = RHS

so two line are perpendicular