Help plz I need it it’s hard

Help! It says that I need to determine If both equations represent lines which are parallel, perpendicular, or none...

12345 [234]

4x + 2y = 8 (1)
 8x + 4y = -4y (2)

A) Two lines are parallel if they have the same gradient
- putting both equations into the gradient- intercept form ( y = mx + c where m is the gradient)
(1) 4x + 2y = 8
 2y = 8 - 4x
y = -2x + 4

 (2) 8x + 4y = -4y
 8x = -4y - 4y
y = $\frac{-8x}{-8}$
y = -x
Thus the gradient of the two equations are different and as such the two lines are not parallel

B) When two lines are perpendicular, the product of their gradient is -1
$m_{1} * m_{2} = p$
p = (-2) * (-1)
p = 2
 ∴ the two lines are not perpendicular either.

Thus these lines are SKEWED LINES

4 0

3 years ago

2y = 4x - 8 3x + 2y = 6 graph

Vinvika [58]

Answer:

see attached

Step-by-step explanation:

I find it convenient to let a graphing calculator draw the graph (attached).

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If you're drawing the graph by hand, there are a couple of strategies that can be useful.

The first equation is almost in slope-intercept form. Dividing it by 2 will put it in that form:

y = 2x -4

This tells you that the y-intercept, (0, -4) is a point on the graph, as is the point that is up 2 and right 1 from there: (1, -2). A line through those points completes the graph.

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The second equation is in standard form, so the x- and y-intercepts are easily found. One way to do that is to divide by the constant on the right to get ...

x/2 +y/3 = 1

The denominators of the x-term and the y-term are the x-intercept and the y-intercept, respectively. If that is too mind-bending, you can simply set x=0 to find the y-intercept:

0 +2y = 6

y = 6/2 = 3

and set y=0 to find the x-intercept

3x +0 = 6

x = 6/3 = 2

Plot the intercepts and draw the line through them for the graph of this equation.

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Here, we have suggested graphing strategies that don't involve a lot of manipulation of the equations. The idea is to get there as quickly as possible with a minimum of mistakes.