Question

the map shows Hope road and the construction site for the new library find the equation of a street that passes through the building site and is parallel to the Hope road​

Answer 1

Answer: $x-3y+12.5=0$

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 :-

$\text{Slope}=\dfrac{\text{Change in y-coordinate}}{\text{Change in x-coordinate}}\\\\\Rightarrow\ \text{Slope}=\dfrac{7-6}{3-0}=\dfrac{1}{3}$

Since , a street that passes through the building site and is parallel to the Hope road​, then the slope of the street will be :-

$m=\dfrac{1}{3}$

[ The two parallel sides have same slopes. ]

Now, the equation of line having slope $m=\dfrac{1}{3}$ and passing through (7,6.5) is given by :-

$(y-6.5)=\dfrac{1}{3}(x-7)\\\\\Rightarrow3(y-6.5)=x-7\\\\\Rightarrow\ 3y-19.5=x-7\\\\\Rightarrow x-3y+12.5=0$

Hence, the equation of a street that passes through the building site and is parallel to the Hope road​  : $x-3y+12.5=0$

Answer 2

Answer: y=1/3x+4

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