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 (−2, 4). find the equation of the location of the second street in standard form.

Answer 1

To find the equation of the location of the second street in standard form, we need to determine the slope of the first street and use it to represent the slope of the second street. By substituting the x and y values of a point on the second street, we can solve for the y-intercept and create the complete equation. The equation of the location of the second street in standard form is y = 3x + 10.

Step-by-step explanation:

To find the equation of the location of the second street in standard form, we need to determine the slope of the first street. Since the second street is parallel to the first street, it will have the same slope. Let's assume the equation of the first street is y = mx + b, where m represents the slope.

We know that the second street passes through the point (-2, 4). This means that when x = -2, y = 4. Substituting these values into the equation, we get:

4 = m(-2) + b

Next, we need to find the slope (m). Since the streets are parallel, the slope of the second street will be the same as the slope of the first street. So, we can use the slope from the first street to represent the slope of the second street. Once we determine the value of m, we can substitute it in the equation and solve for b to find the complete equation in standard form.

Let's assume the slope of the first street is 3. Plugging in the values, we get:

4 = 3(-2) + b

Simplifying the equation, we have:

4 = -6 + b

Adding 6 to both sides of the equation, we get:

10 = b

Now we have the values for m and b. Plugging these values into the equation, we get:

y = 3x + 10

Therefore, the equation of the location of the second street in standard form is y = 3x + 10.

Answer 2

A contractor is building a new subdivision on the outside of a city, the equation of the location of the second street in standard form is mx - y + 2m - 4 = 0.

Step-by-step explanation:

To find the equation of the location of the second street, we need to determine its slope and y-intercept.

Since the second street passes through the point (-2, 4), we can use this information to find the slope.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:

slope = (y2 - y1) / (x2 - x1)

Now plugging in the values (-2, 4) as the first point and assume (-x, y) as the second point:

slope = (y - 4) / (x - (-2))

slope = (y - 4) / (x + 2)

Since the new street is parallel to the first street, the slopes of the two streets are equal. Therefore, we can equate the two slopes:

(y - 4) / (x + 2) = m

The standard form of a linear equation is Ax + By = C.

To convert the slope-intercept form to standard form, we multiply both sides of the equation by (x + 2) to get:

y - 4 = m(x + 2)

y - 4 = mx + 2m

mx - y + 2m - 4 = 0

Therefore, the equation of the location of the second street in standard form is mx - y + 2m - 4 = 0.