Answer:
Part 1)
Part 2) The equation in point slope form is equal to and the equation in slope intercept form is equal to
Part 3) The system of equations is a consistent independent system
Part 4) The coordinates of the intersection point are x=1 and y=5
Step-by-step explanation:
Part 1) Write the equation of the sidewalks 1 in slope intercept form
we know that
The equation of the line in slope intercept form is equal to
where
m is the slope
b is the y-intercept
we have the points
(2,7) and (0,3)
Find the slope
The formula to calculate the slope between two points is equal to
substitute the values
The y-intercept is the point (0,3)
so
substitute
Part 2) Write the equation of the sidewalks 2 in point slope form and then in slope intercept form
The equation in point slope form is equal to
Find the slope
we have the points
(1,5) and (3,3)
substitute in the formula
take the point (1,5)
substitute
----> equation in point slope form
Convert to slope intercept form
Isolate the variable y
Adds 5 both sides
---> equation in slope intercept form
Part 3) Is the system of equations consistent independent, coincident or inconsistent
we have
-----> equation A
-----> equation B
Remember that the solution of the system is the intersection point both graphs
The slopes of the lines of the system are different, that means that the lines are not parallel, so the system has one solution (one intersection point)
Remember that
If a system has at least one solution, it is said to be consistent
If a consistent system has exactly one solution, it is independent
therefore
The system of equations is a consistent independent system
Part 4) Use the substitution method to solve the system
we have
-----> equation A
-----> equation B
substitute equation A in equation B
solve for x
Group terms
Find the value of y
substitute the value of x in equation A or equation B (is the same)
The solution is the point (1,5)
therefore
The coordinates of the intersection point are x=1 and y=5