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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?

User John Owen
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1 Answer

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Answer:


y=x+3

Explanation:

Hi there!

What we need to know:

  • Linear equations are typically organized in slope-intercept form:
    y=mx+b 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)


x-y=5

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


x-y-x=-x+5\\-y=-x+5

Divide both sides by -1 to isolate y


y=x-5

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
y=mx+b:


y=1x+b\\y=x+b

2) Determine the y-intercept (b)


y=x+b

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


-2=-5+b

Add 5 to both sides


-2+5=-5+b+5\\3=b

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


y=x+3

I hope this helps!

User Tmtrademark
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