The dimensions of the Japanese flag (or Nisshoki) are in a ratio of 2:3.
If the shorter side of the flag is 5
feet, find the length of the diagonal.

A.

B. Point Slope Form: and Slope-Intercept Form:

C. Independent

D.

Step-by-step explanation:

Given 2 points on Sidewalk 1: and .

Given 2 points on Sidewalk 2: and

Where,

m is the slope, and [NOTE: is point 1 and is point 2]

b is the y-intercept [point where the line crosses the y-axis]

Where,

m is the slope, and

is point 1

A.

Slope-Intercept from is given by

Finding m using formula above gives us:

Plugging in any one point, let us substitute , in x and y respectively gives us value of b:

Now we can write:

B.

Solving for m for sidewalk 2 using points above and slope formula, we get:

Point-Slope form using formula above:

Rearranging this in slope-intercept form, we have:

C.

2 lines DOES NOT have any solution when:

1. They are the same line [coefficients of one line are multiple of coefficient of another line ]

2. They are parallel [ when slope of one line is equal to slope of another line ]

Here, none of these occurs, so we HAVE a solution.

Hence, the system of equations are said to be INDEPENDENT.

D.

Since, the 2 equations have a solution [they have an intersection point], let's solve for the intersecting point.

We have the equations and

We set both of them equal [y=y] and solve for x:

Now substitute this value of x into either equation to get y. Let's do it on equation 1:

So, point of intersection is