Question

the information given. When applicable, eraph the equations.2m =4y=2x-16aŭ= 28 b=_-16Equation of Line: 4y - 2x = 16Rewritten: ya2x-16Im =2x + m = -2I lineI line

Answer 1

From the given equation :

`4y-2x=16`

This can be written in the slope-intercept form :

`y=mx+b`

where m is the slope

and b is the y-intercept

Rewriting the equation :

`\begin{gathered} 4y-2x=16 \\ 4y=2x+16 \\ y=(2)/(4)x+(16)/(4) \\ y=(1)/(2)x+4 \end{gathered}`

The equation will be y = 1/2 x + 4

the slope is m = 1/2

nd the y-intercept is b = 4

Note that parallel lines have the same slope.

So the slope of parallel line is m = 1/2

Perpendicular lines have a slope of negative reciprocal with each other.

So the slope of perpendicular line to this line is m = -2

Equation of parallel line :

we have :

`y=(1)/(2)x+b`

Let's say the line passes at the origin (0, 0)

If a line passes thru the origin, the y-intercept is always b = 0

Therefore, the equation of parallel line is y = 1/2 x

quation of perpendicular line :

we have :

`y=-2x+b`

Let's also say that the line passes at the origin (0, 0)

and the y-intercept is also b = 0

he equation of the perpendicular line is yy = -2x

raphing these equations will be :

Original line (Blue)

Parallel line (Orange)

Perpendicular line (Pink)

y-intercepts :

(0, 0) and (0, 4)