Two sidewalks in a park are represented by lines on a coordinate grid. two points on each of the lines are shown in the tables. sidewalk sidewalk (a) write the equation for sidewalk 1 in slope - intercept form. (b) write the equation for sidewalk 2 in point - slope form and then in slope - intercept form. (c) is the system of equations consistent independent, coincident, or inconsistent? explain. (d) if the two sidewalks intersect, what are the coordina tes of the point of intersection? use the substitution method and show your work

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

the slope of the line is 60

one point on the line is (40,10)

step-by-step explanation:

in the equation outside the parenthesis the equation always tells you the slope. in this case it is 60.

in the parenthesis is also says 40 which is x because it is near the x and 10 is y because it is near y.