To determine the equation of the second street in standard form, passing through the point [tex]\((-5, -1)\)[/tex] and running parallel to the first street, we follow these steps:
1. Identify the Characteristics of Parallel Streets:
- Parallel streets have the same slope. Assuming the first street has a particular orientation, we know that the slope will be consistent.
2. Consider the Standard Form of a Linear Equation:
- The standard form of a linear equation is given as [tex]\(Ax + By = C\)[/tex].
- For simplicity, let's assume the first street is vertical. A vertical line has an undefined slope and its equation is of the form [tex]\(x = k\)[/tex], where [tex]\(k\)[/tex] is a constant.
3. Determine the Equation of the Street:
- Since the second street is parallel to the first and passes through the point [tex]\((-5, -1)\)[/tex], it must also be a vertical line.
- For a vertical line passing through the point [tex]\((-5, -1)\)[/tex], the equation is [tex]\(x = -5\)[/tex].
4. Convert to Standard Form:
- The standard form requires the equation to be in the form [tex]\(Ax + By = C\)[/tex]. A vertical line [tex]\(x = -5\)[/tex] can be rewritten as:
[tex]\[1 \cdot x + 0 \cdot y = -5\][/tex]
- Here, [tex]\(A = 1\)[/tex], [tex]\(B = 0\)[/tex], and [tex]\(C = -5\)[/tex].
Therefore, the equation of the second street in standard form is:
[tex]\[ 1x + 0y = -5 \][/tex]
So, the standard form equation of the street passing through [tex]\((-5, -1)\)[/tex] and running parallel to the first street is [tex]\(x = -5\)[/tex], which translates to [tex]\(1x + 0y = -5\)[/tex] in standard form.
