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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​

the map shows Hope road and the construction site for the new library find the equation-example-1

2 Answers

3 votes

Answer: y=1/3x+4

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User Pawel Urban
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7.8k points
2 votes

Answer:
x-3y+12.5=0

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}=\frac{\text{Change in y-coordinate}}{\text{Change in x-coordinate}}\\\\\Rightarrow\ \text{Slope}=(7-6)/(3-0)=(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=(1)/(3)

[ The two parallel sides have same slopes. ]

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


(y-6.5)=(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

User Ryan Coolwebs
by
8.1k points

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