Question

a contractor is building a new subdivision on the outside of a city. he has started work on the first street and is planning for the other streets to run in a direction parallel to the first. the second street will pass through (−5, −1). find the equation of the location of the second street in standard form. coordinate grid with a segment labeled street 1 that extends between the points negative 5 comma 6 and three comma negative 2; a point labeled street 2 is at negative 5 comma negative 1

Answer 1

The equation of the location of the second street in standard form is

x + y = -6

Equation of the line:

The equation of the line represents the algebraic form of representing the set of points, which together form a line in a coordinate system.

The equation of the line can be formed with the help of the slope of the line and a point on the line.

The general form of the equation of a line with a slope m and passing through the point (x₁,y₁) is given as:

y = mx + b.

Where

m represents the slope of the line.

Given,

Point = ( -5 , -1)

Here we need to find the equation of the location.

For that, first we have to find the slope of the line,

Having two points in the format (x,y), the slope is given by the change in y divided by the change in x.

The equation of the street is parallel to the equation of the line in the graph, thus they have the same slope.

So, in street 1 the equation is

=> y =-x +1

And street 2 the equation is  

=> y =-x +b,  

solve for b by plugging in (-5,-1)

=> -1 =-(-5) +b

=> b= -1-5 = -6

=> b = -6

Now apply the value of b on the equation,

Then

=> y = -x -6

=> y + x = -6

So, the equation of the location is x + y = -6.

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