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!
