Write the equations of five lines that are parallel to [tex]y = \frac{x}{2} - 6[/tex].

(Note: Parallel lines have the same slope. Therefore, the slope of each line should be [tex]\frac{1}{2}[/tex].)

1. [tex]y = \frac{x}{2} + c_1[/tex]
2. [tex]y = \frac{x}{2} + c_2[/tex]
3. [tex]y = \frac{x}{2} + c_3[/tex]
4. [tex]y = \frac{x}{2} + c_4[/tex]
5. [tex]y = \frac{x}{2} + c_5[/tex]

Where [tex]c_1, c_2, c_3, c_4,[/tex] and [tex]c_5[/tex] are constants that can be chosen to give different y-intercepts for each line.

If two lines are parallel, then they must have the same slope. So, let's take the equation y=1/2x-6(equal to y=x/2-6) and just change the y intercept

y=1/2x 2.y=1/2x+3 3.y=1/2x-7 4.y=1/2x+4 5.y=1/2x-8 and so on...

Answered by MiNk2019314 | 2024-06-10

To find parallel lines to y=x/2-6, we just need to change the y-intercept, b, in the equation y=mx+b where m is the slope. The five equivalent equations could be y = x/2 - 3, y = x/2 + 1, y = x/2 + 5, y = x/2 - 10, and y = x/2 + 7. ;

Answered by arshise58 | 2024-06-18

The equations of five lines parallel to y = 2 x ​ − 6 can be found by maintaining the same slope of 2 1 ​ but varying the y-intercepts. The resulting equations are: y = 2 x ​ + 0 , y = 2 x ​ + 3 , y = 2 x ​ − 2 , y = 2 x ​ + 5 , and y = 2 x ​ − 8 . All these lines will run parallel to the original line without ever intersecting it.
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Answered by arshise58 | 2024-10-10