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: y=1/3x+4

You're welcome

Answer 2

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`