Answer:
[tex]y=\frac{1}{3}x +5[/tex]
Step-by-step explanation:
Linear equations are typically formatted in slope-intercept form:
[tex]y=mx+b[/tex] where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope (m)
Parallel lines will always have the same slope. Therefore, this line will also have a slope of [tex]\frac{1}{3}[/tex]. Plug this into our equation:
[tex]y=\frac{1}{3} x+b[/tex]
2) Determine the y-intercept (b)
To solve for the y-intercept (b), plug the given point (-3,4) into our equation and isolate b.
[tex]4=\frac{1}{3}(-3)+b\\4=\frac{-3}{3}+b\\4=-1+b[/tex]
Add 1 to both sides
[tex]4+1=-1+b+1\\5=b[/tex]
Therefore, the y-intercept is 5. Plug this back into our original equation with the slope:
[tex]y=\frac{1}{3}x +5[/tex]
I hope this helps!
