Question

Find the equation of a “street”that passes through the building site and is parallel Santa Cruz boulevard?

Answer 1

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

Step-by-step explanation

We simply want to find the equation of the line that is parallel to the given line and passes through the given point (4, 1).

A line that is parallel to another line has the same slope as that line.

So, we have to find the slope of the given line using the formula:

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

where (x₁, y₁) and (x₂, y₂) are two points that line on the line.

Let us pick the points (0, 4) and (4, 6)

Therefore, the slope is:

`\begin{gathered} m=(6-4)/(4-0)=(2)/(4) \\ m=(1)/(2) \end{gathered}`

Now, we apply the point-slope method to find the equation of the line:

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

where (x₁, y₁) is the point.

From the graph, the point is (4, 1).

Therefore, the equation of the line is:

`\begin{gathered} y-1=(1)/(2)(x-4) \\ y-1=(1)/(2)x-(4)/(2) \\ y=(1)/(2)x-2+1 \\ y=(1)/(2)x-1 \end{gathered}`