Lizcurlycuzgidn
Answered

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What is an equation of the line that passes through the point (-5,-2)and is parallel to the line x-y=5?

Sagot :

Theleangreenbeanidn

Answer:

[tex]y=x+3[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

  • Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
  • Parallel lines always have the same slope (m)

1) Determine the slope (m)

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

Rearrange this given equation into slope-intercept form. This will make it easier for us to identify the slope.

Subtract x from both sides of the equation

[tex]x-y-x=-x+5\\-y=-x+5[/tex]

Divide both sides by -1 to isolate y

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

Now, we can identify clearly that the slope of this line is 1. Because parallel lines have the same slopes, a line parallel to this one would also have a slope of 1. Plug this into [tex]y=mx+b[/tex]:

[tex]y=1x+b\\y=x+b[/tex]

2) Determine the y-intercept (b)

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

Plug in the given point (-5,-2)

[tex]-2=-5+b[/tex]

Add 5 to both sides

[tex]-2+5=-5+b+5\\3=b[/tex]

Therefore, the y-intercept of the line is 3. Plug this back into [tex]y=x+b[/tex]:

[tex]y=x+3[/tex]

I hope this helps!

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