Question

The map shows Santa Cruz Boulevard and the construction site for the new town hall. Find the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard.

Answer 1

y=1/2x-1 is the answer that is parallel

Answer 2

the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard
`y=(x)/(2)+4`

Explanation:

• The slope is find by 2 points on line
  `(x_1,y_1)\,\text{and}\,(y_2,y_2)` is calculated as;
  `m=(y_2-y_1)/(x_2-x_1)`

• Equation of line is in slope-intercept form is written as;

`(y-y_1)=m(x_2-x_1)`

We can easily take two points from given graphs are

(2,5) and (6,7)

The slope of line is;

`m=(y_2-y_1)/(x_2-x_1)`

`m=(7-5)/(6-2)`

`m=(2)/(4)`

`m=(1)/(2)`

the slope of line is
`(1)/(2)`

Now, find the equation of line with the slope-intercept form

`(y-y_1)=m(x-x_1)`

`(y-5)=(1)/(2)(x-2)`

Add both the sides by 5 in above expression,

`y=(1)/(2)(x-2)+5`

`y=(x)/(2)-1+5`

`y=(x)/(2)+4`

Therefore, the equation of a “street” that passes through the building site and is parallel to Santa Cruz Boulevard
`y=(x)/(2)+4`