Answer:
y = [tex]\frac{4}{5}x+\frac{54}{5}[/tex]
Step-by-step explanation:
Equation of a line has been given as,
[tex]y=\frac{4}{5}x+\frac{3}{5}[/tex]
Here, slope of the line = [tex]\frac{4}{5}[/tex]
y-intercept = [tex]\frac{3}{5}[/tex]
"If the two lines are parallel, there slopes will be equal"
By this property slope of the parallel line to the given line will be equal.
Therefore, slope 'm' = [tex]\frac{4}{5}[/tex]
Since, slope intercept form of a line is,
y = mx + b
Therefore, equation of the parallel line will be,
y = [tex]\frac{4}{5}x+b[/tex]
Since, this line passes through a point (-6, 6),
6 = [tex]\frac{4}{5}(-6)+b[/tex]
6 = [tex]-\frac{24}{5}+b[/tex]
b = [tex]6+\frac{24}{5}[/tex]
b = [tex]\frac{30+24}{5}[/tex]
b = [tex]\frac{54}{5}[/tex]
Equation of the parallel line will be,
y = [tex]\frac{4}{5}x+\frac{54}{5}[/tex]