Answer:
The equation of line 'U' is;
y = [tex]\frac{x}{9}[/tex] + 5
Step-by-step explanation:
A line 'T' has an equation; y = [tex]\frac{1}{9}[/tex]x - 9
A line 'U' passes through point (4,1) and is parallel to the line 'T'
We are to find the equation of line 'U'.
The slopes of two parallel lines are equal.
The slope of line 'T' is [tex]\frac{1}{9}[/tex] and so the slope of line 'U' is [tex]\frac{1}{9}[/tex]
Since line 'U' passes through point (4,1) , we choose another point (x,y) still on the line.
Slope = change in y ÷ change in x
[tex]\frac{1}{9}[/tex] = [tex]\frac{y - 1}{x - 4}[/tex]
Cross-multiplying gives;
9y - 9 = x - 4
9y = x - 4 + 9
9y = x + 5
y = [tex]\frac{1}{9} x[/tex] + 5 (and this is the equation of line 'U')
