It can be hard to graph functions when the y-intercept is not an integer.
B
b
As the x-values increase, the y-value of the second equation decreases.
C
c
Graphing will require estimating a solution.
A
a
(-1, 3)
B
b
(2,2)
C
c
(-1.5,0.5)
Practice makes perfect
a
The non-integer slope and y-intercept will make this system rather difficult to graph, which may mean that that we have to estimate the solution. Let's use a table to find the solution to this system.
x
- 4.3x-1.3
y
1.7x+4.7
y
1
- 4.3* 1-1.3
- 5.6
1.7* 1+4.7
6.4
0
- 4.3* 0-1.3
-1.3
1.7* 0+4.7
4.7
- 1
- 4.3( - 1)-1.3
3
1.7( - 1)+4.7
3
Thus the solution is (-1, 3). Let's verify this with our graphing calculator. First we have to enter the equations into the calculator. To do that, we press the Y= button and write the equations on the two first rows.
Now we can plot them by pressing GRAPH.
Next, to find the point of intersection, we press CALC, 2nd, then TRACE and choose the fifth option in the menu, intersect.
We will see the graph again. Now we have to select the first and second curve before guessing where the point of intersection is. Make sure to place the cursor as close as possible to the point of intersection before pressing ENTER again.
We have now confirmed that the solution to the system of equations is (-1, 3).
b
Since these functions will be easy to graph, let's solve this system using a graph. We graph both functions on the same coordinate plane and find the point of intersection.
The solution is (2,2). We can check the point of intersection using our graphing calculator using the same method as in the first exercise.
We have now confirmed that the solution to the system of equations is (2,2).
c
This system should also be easy to graph, so let's use a graph again.
Since the point of intersection is not directly on grid lines, we need to estimate the solution. It looks to approximately be (-1.5,0.5). Using the same method as in the first exercise, we can check the point of intersection using our graphing calculator.
We have now confirmed that the solution to the system of equations is (-1.5, 0.5).
