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 (1, 5). 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 1 comma 5 x y = 6 2x y = 7 x − y = 6 2x − y = 7.

Answer 1

You can use those two given points of street 1 to form its equation, then can use the fact that parallel lines have same slope to find the equation of second street with the help of the point (1,5) which lies in second street.

The equation of the location of the second street in standard form is given as $2y = x + 9$

What is the equation of a straight line passing through two given points?

Let the two given points be (a,b) and (c,d). Then the equation of straight line passing through these two points is given by:

$y - b = \dfrac{(d-b)}{(c-a)}(x-a)$

What is slope intercept form of equation of straight line?

y = mx + c is the slope intercept form of straight line where m is the slope and c is the y-intercept (where the straight line cut on y = c at y axis) of the given line.

How to find equation of second street's location in terms of equation of straight line?

Firstly we will find the equation of straight line which represents street 1.

Since street 1 goes from point (-5,-6) and (3,-2), thus, its equation would be:

$y - (-6) = \dfrac{-2- (-6)}{3-(-5)} (x -(-5))\\ \\ y + 6 = \dfrac{1}{2}(x+5)\\ \\ y + 6 = \dfrac{x}{2} + \dfrac{5}{2}\\\\ y = \dfrac{x}{2} -\dfrac{7}{2}$

Thus, this above equation represents equation of location of street 1. The slope is 1/2 and y-intercept is -7/2.

Since the street 2 is parallel to street 1, thus we have its slope same as that of street 1. Writing the equation in slope intercept form we get:

$y = \dfrac{1}{2}x + c$

Since street 2 passes through (1,5)( x=  1, y = 5), thus, this point must satisfy above equation which represents all points lying on street 2.

Thus,

$5 = \dfrac{1}{2} \times 1 + c\\\\ c = 5 - \dfrac{1}{2} = \dfrac{9}{2}$

Thus, the equation representing points on street 2 is given by:

$y = \dfrac{x}{2} + \dfrac{9}{2}\\ \\ 2y = x + 9$

Learn more about equation of straight line here:

https://brainly.com/question/19380936