Answer:
[tex]y=\frac{4}{7}x-4[/tex]
Step-by-step explanation:
1. Find the slope of the parallel line.
The general form to the equation of the line is given by [tex]y=mx+b[/tex] where m is the slope.
If you need to find a parallel line it has the same slope.
As the problem gives the equation of the line [tex]y=\frac{4}{7}x-3[/tex] it means that the slope of the line and its parallel is [tex]m=\frac{4}{7}[/tex].
2. Find the equation of the parallel line.
The line must pass through the point (14,4).
Let´s name it as:
[tex]x_{1}=14[/tex]
[tex]y_{1}=4[/tex]
Replacing these values in the point-slope equation we have:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y-4=m(x-14)[/tex]
[tex]y-4=\frac{4}{7}(x-14)[/tex]
Solving for y:
[tex]y-4=\frac{4}{7}x-\frac{56}{7}[/tex]
[tex]y-4=\frac{4}{7}x-8[/tex]
[tex]y=\frac{4}{7}x-8+4[/tex]
[tex]y=\frac{4}{7}x-4[/tex]
