Answer:
[tex]y=x+4[/tex]
Step-by-step explanation:
Two parallel lines will have the same slope:
[tex]y=mx+b[/tex]
This is the y-intercept equation, where m is the slope and b is the y-intercept:
[tex]y=x+3[/tex]
The slope is x, or 1x, so the parallel line is also x.
Find the y-intercept:
You do this by taking the equation given and solving for y:
[tex]2x+3y=12[/tex]
Isolate the variable y. Subtract 2x from both sides:
[tex]2x-2x+3y=12-2x\\\\3y=12-2x[/tex]
Isolate y by dividing both sides by 3:
[tex]\frac{3y}{3}=\frac{12}{3}-\frac{2x}{3} \\\\y=4-\frac{2}{3}x[/tex]
Rearrange in slope-intercept form:
[tex]y=-\frac{2}{3}x+ 4[/tex]
The y-intercept of this equation is 4.
Now make the equation using the given information:
[tex]y=x+4[/tex]
:Done
