Question

The city is planning to create a new street which will be parallel to Vine Street. Write an equation that could represent the new street? (Hint: Find the slope of the line of Vine St.)

Answer 1

Given:

The objective is to find the equation of parallel line for the given figure.

First, let's find the slope of the given line.

It is known that the equation of slope is,

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

Consider two coordinates from the given graph.

`\begin{gathered} (x_1,y_1)=(4,4) \\ (x_2,y_2)=(8,6) \end{gathered}`

Substitute the value in the equation of slope.

`\begin{gathered} m=(6-4)/(8-4) \\ m=(2)/(4) \\ m=(1)/(2) \end{gathered}`

From the given graph, the y-intercept is 2.

The general equation of straight line is,

`y=mx+c`

Here, m stands for slope and c stands for y intercept.

Substitute the obtained values in the equation of straight line.

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

Thus, the equation of given striaght line is obtained.

To find the eqution of its parallel line, consider y intercept of new parallel line at -1.

For parallel lines, the slope values will be equal.

So take slope value of new parallel line as m = 1/2.

Then, the equation of new parallel line will be,

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

Hence, the equation of parallel line will be y=(1/2)x-1.