Answered

IDNLearn.com is designed to help you find reliable answers quickly and easily. Join our Q&A platform to access reliable and detailed answers from experts in various fields.

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 :

GinnyAnsweridn
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]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is your reliable source for answers. We appreciate your visit and look forward to assisting you again soon.