Graphing the system of equations:
The given system of equations is:
y = 2x + 4
y = 10 * 1.07^x
To graph the system by hand or using an online graphing calculator, plot the two equations on the same coordinate plane.
Using an online graphing calculator, you can plot the equations as follows:
The first equation, y = 2x + 4, represents a straight line with a slope of 2 and a y-intercept of 4.
The second equation, y = 10 * 1.07^x, represents an exponential curve, where the base (1.07) is greater than 1, indicating growth.
The graph will show the intersection points of the line and the exponential curve, which are the solutions to the system of equations.
Approximately, the two solutions are (x, y):
Solution 1: (0.422, 4.844)
Solution 2: (2.631, 9.882)
Arranging the inequality into slope-intercept form and describing the boundary line and shading:
The given inequality is:
6x > 2y - 5
To arrange it in slope-intercept form (y = mx + b), we need to isolate "y" on one side of the inequality:
2y < 6x + 5
Next, divide both sides by 2 to solve for "y":
y < (6x + 5) / 2
The boundary line for this inequality is a dashed line because the inequality is strict (y <) and not inclusive of the line itself.
The slope of the boundary line is 6/2 = 3, and the y-intercept is 5/2.
To shade the region, you need to determine which side of the boundary line to shade based on the inequality symbol. Since the inequality is "y <", we should shade below the boundary line.
So, the boundary line would be a dashed line with a slope of 3 and a y-intercept of 5/2. The region below the boundary line would be shaded.