Answer:
[tex]y=\frac{1}{2} x+1[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
- Parallel lines have the same slope and different y-intercepts
1) Determine the slope (m)
Rewrite [tex]2x -4y =12[/tex] in slope-intercept form. This will make it easier for us to identify the slope.
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)
[tex]2x -4y =12[/tex]
Subtract 2x from both sides to isolate -4y
[tex]2x -4y-2x =-2x+ 12\\-4y=-2x+ 12[/tex]
Divide both sides by -4 to isolate y
[tex]-4y=-2x+ 12\\y=\frac{1}{2}x -3[/tex]
Now, we can see clearly that [tex]\frac{1}{2}[/tex] is in the place of m in [tex]y=mx+b[/tex] , making it the slope of the line.
Because parallel lines have the same slopes, we know that the line we're determining will also have a slope of [tex]\frac{1}{2}[/tex].
2) Determine the y-intercept (b)
Plug [tex]\frac{1}{2}[/tex] into [tex]y=mx+b[/tex]
[tex]y=\frac{1}{2} x+b[/tex]
Plug in the given point (4,3)
[tex]3=\frac{1}{2} (4)+b\\3=2+b[/tex]
Subtract 2 from both sides
[tex]3-2=2+b-2\\1=b[/tex]
Therefore, the y-intercept (b) is 1. Plug this back into [tex]y=\frac{1}{2} x+b[/tex]
[tex]y=\frac{1}{2} x+1[/tex]
I hope this helps!
