Answer: [tex]x-3y+12.5=0[/tex]
Step-by-step explanation:
From the give en graph , the coordinates of the point marked for library =(7,6.5)
The slope of the Hope road passing from points (0,6) and (3,7) is given by :-
[tex]\text{Slope}=\dfrac{\text{Change in y-coordinate}}{\text{Change in x-coordinate}}\\\\\Rightarrow\ \text{Slope}=\dfrac{7-6}{3-0}=\dfrac{1}{3}[/tex]
Since , a street that passes through the building site and is parallel to the Hope road, then the slope of the street will be :-
[tex]m=\dfrac{1}{3}[/tex]
[ The two parallel sides have same slopes. ]
Now, the equation of line having slope [tex]m=\dfrac{1}{3}[/tex] and passing through (7,6.5) is given by :-
[tex](y-6.5)=\dfrac{1}{3}(x-7)\\\\\Rightarrow3(y-6.5)=x-7\\\\\Rightarrow\ 3y-19.5=x-7\\\\\Rightarrow x-3y+12.5=0[/tex]
Hence, the equation of a street that passes through the building site and is parallel to the Hope road : [tex]x-3y+12.5=0[/tex]
