Answer:
[tex]y=2x+2[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
1) Determine the slope (m)
[tex]2x-y = 5[/tex]
To do so, we must organize the given equation into slope-intercept form to identify the value in place of m.
Subtract 2x from both sides (isolate y)
[tex]2x-y -2x= -2x +5\\-y= -2x +5[/tex]
Divide both sides by -1 (isolate y)
[tex]y= 2x -5[/tex]
Now, from this equation, we can tell that the number in the place of m in [tex]y=mx+b[/tex] is 2. Because parallel lines have equal slopes, the slope of the line we're currently solving for would also be 2. Plug this slope into [tex]y=mx+b[/tex]:
[tex]y=2x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=2x+b[/tex]
Plug in the given point (-3,-4) and solve for b
[tex]-4=2(-3)+b\\-4=-6+b[/tex]
Add 6 to both sides to isolate b
[tex]-4+6=-6+b+6\\2=b[/tex]
Therefore, the y-intercept is 2. Plug this back into [tex]y=2x+b[/tex]:
[tex]y=2x+2[/tex]
I hope this helps!
