Question

tell whether the lines for each pair of equations are parallel perpendicular or neither
7x - 4y= 4
x - 4y= 3

Answer 1

`1.` Isolate y in each equation so that they have the form y = mx + b
`2.` If the slopes are equal to each other, then both lines are parallel. If the product of the slopes of both equations is -1, then the lines are perpendicular.

`1.`

Equation 1:
7x - 4y = 4

Add 4y to both sides; Subtract 4 from both sides:
7x - 4 = 4y

Divide both sides by 4:
\[\frac{7x - 4}{4} = y\]
\[\frac{7x}{4} - 1 = y\]

Equation 2:
x - 4y = 3

add 4y to both sides; subtract 3 from both sides:
x - 3 = 4y

Divide both sides by 4:
\[\frac{x - 3}{4} = y\]
\[\frac{x}{4} - \frac{3}{4} = y\]

`2.` The slopes of both equations are \(m_1 = \frac{7}{4}\) and \(m_2 = \frac{1}{4}\). Clearly their slopes are not the same. Both slopes are positive so their products will not be negative. Thus the lines are neither parallel nor perpendicular.

Answer 2

@Hero Thank you so much