Question

Please answer the questions below

Answer 1

Answer:

see explanation

Step-by-step explanation:

(3)

Parallel lines have equal slopes

the equation of a line in sloipe- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = $\frac{1}{4}$ x + 5 ⇒ m = $\frac{1}{4}$

y = 4x + 5 ⇒ m = 4

y = - 4x + 5 ⇒ m = - 4

y = - 4x - 9 ⇒ m = - 4

the 3rd and 4th options have equal slopes and are parallel

(4)

given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$

y = $\frac{1}{6}$ x + 4 ⇒ m = $\frac{1}{6}$

y = - $\frac{1}{6}$ x + 5 ⇒ m = - $\frac{1}{6}$

y = $\frac{1}{6}$ x + 3 ⇒ m = $\frac{1}{6}$

y = 6x + 3 ⇒ m = 6

note that a slope of m = 6 , has a perpendicular slope of

$m_{perpendicular}$ = - $\frac{1}{6}$

the 2nd and 4th lines are perpendicular