Answer:Part a)
Part b) The equation in point slope form is and the equation in slope intercept form is
Part c) The system is consistent independent
Part d) The coordinates of the point of intersection are x=1 and y=5
Explanation:
Part a) Write the equation for Sidewalk 1 in slope-intercept form
we know that
The equation of the line in slope intercept form is equal to
Find the slope m
we have the points
(2,7) and (0,3)
The y-intercept is the point (0,3)
so
substitute
Part b) Write the equation for Sidewalk 2 in point-slope form and then in slope-intercept form
step 1
The equation of the line in point slope form is equal to
Find the slope m
we have the points
(1,5) and (3,3)
take the point (1,5)
substitute
step 2
Convert the equation in slope intercept form
Isolate the variable y
Part c) Is the system of equations consistent independent, coincident, or inconsistent?
we have
----> equation A
----> equation B
we know that the lines are not parallel (the slopes are different), therefore will intersect at a single point, and the system will have only one solution
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 .
If a consistent system has an infinite number of solutions, it is dependent
If a system has no solution, it is said to be inconsistent
therefore
In this problem the system is consistent independent
Part d) Use the substitution method to solve your system. If the two sidewalks intersect, what are the coordinates of the point of intersection?
we have
----> equation A
----> equation B
Substitute equation A in equation B
Solve for x
Find the value of y
substitute the value of x
The solution is the ordered pair (1,5)
therefore
The coordinates of the point of intersection are x=1 and y=5
Explanation: