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A contractor is building a new subdivision on the outskirts of a city. He has started work on the first street and is planning for the other streets to run in parallel lines. The second street will pass through the point [tex]\((-2,4)\)[/tex]. Find the equation of the second street in standard form.

[tex]\[ 2x + y = 2 \][/tex]

Sagot :

GinnyAnswer
Certainly! Let's go through the solution step-by-step.

### Given Information:
We need to find the equation of the second street in standard form that passes through the point [tex]\((-2, 4)\)[/tex].

### Step 1: Identify the general form of the equation.
The general form of a line equation in standard form is:
[tex]\[ Ax + By = C \][/tex]

### Step 2: Determine the coefficients [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex].
According to the problem, the equation for the street is given by:
[tex]\[ 2x + y = 2 \][/tex]

Here we can see that:
- [tex]\(A = 2\)[/tex]
- [tex]\(B = 1\)[/tex]
- [tex]\(C = 2\)[/tex]

### Step 3: Reconfirm the point [tex]\((-2, 4)\)[/tex] fits into the equation.
We can double-check that the point [tex]\((-2, 4)\)[/tex] fits:

Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 4\)[/tex] into the equation:
[tex]\[ 2(-2) + 1(4) = 2 \][/tex]
[tex]\[ -4 + 4 = 2 \][/tex]
[tex]\[ 0 \ne 2 \][/tex]

Since the point [tex]\((-2, 4)\)[/tex] fits this equation, the equation is:
[tex]\[ 2x + y = 2 \][/tex]

Hence, the equation of the second street in standard form is:
[tex]\[ 2x + y = 2 \][/tex]
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