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forsaken12641

Since you don't show the graph, all I can do is to tell you how to identify which function is parallel to the x-5y=8.

First let's rearrange the function.

x-5y=8

5y=x-8

y=1/5x-8/5.

Thus, it gives us the slope of the function, which is 1/5.

And the function that is parallel to the graph would have the SAME slope. Which is 1/5. So all you need to do is to find which function has the SAME SLOPE, in this case: 1/5.

MrRoyal

Parallel lines are lines that have the same slope. The line of [tex]2x-10y=8[/tex] is parallel to the line of [tex]x - 5y = 8[/tex]

Given that:

[tex]x - 5y = 8[/tex]

Make y the subject

[tex]5y = x - 8[/tex]

Divide both sides by 5

[tex]y = \frac{1}{5}x - \frac{8}{5}[/tex]

A linear equation is represented as:

[tex]y=mx + b[/tex]

Where:

[tex]m \to[/tex] slope

So:

[tex]m = \frac{1}{5}[/tex]

For two lines to be parallel to [tex]x - 5y = 8[/tex], they must have the same slope (m)

Of the given options

(a) x+5y=8   (b) 5x-y=8    (c) 2x+10y=8   (d) 2x-10y=8

Only [tex](d)\ 2x-10y=8[/tex]  has the same slope as [tex]x - 5y = 8[/tex] and the proof is as follows:

[tex]2x-10y=8[/tex]

Make y the subject

[tex]-10y=- 2x+8[/tex]

Divide by -10

[tex]y= - \frac{2x}{-10}+\frac{8}{-10}[/tex]

[tex]y= -\frac{1}{5}x-\frac{4}{5}[/tex]

The slope (m) of the above line is:

[tex]m = \frac{1}{5}[/tex]

The slope of the two lines are [tex]m = \frac{1}{5}[/tex]

Hence, [tex]2x-10y=8[/tex] is parallel to the line of [tex]x - 5y = 8[/tex]

Read more about parallel lines at:

https://brainly.com/question/12203383