Susie determined that the system of equations below has many solutions the first line goes through the points (2,-13) and (-2,-1)
the second lines goes through the points (5,-22) and (-3,2)
To find the equation of the first line, let's first determine the slope using the given points (2,-13) and (-2,-1):
m = (y2 - y1) / (x2 - x1)
m = (-1 - (-13)) / (-2 - 2)
m = 12 / -4
m = -3
Next, let's use one of the points (2, -13) to find the y-intercept (b):
y = mx + b
-13 = -3(2) + b
-13 = -6 + b
-7 = b
Therefore, the equation of the first line is:
y = -3x - 7
To find the equation of the second line, let's first determine the slope using the given points (5,-22) and (-3,2):
m = (y2 - y1) / (x2 - x1)
m = (2 - (-22)) / (-3 - 5)
m = 24 / -8
m = -3
Next, let's use one of the points (5, -22) to find the y-intercept (b):
y = mx + b
-22 = -3(5) + b
-22 = -15 + b
-7 = b
Therefore, the equation of the second line is:
y = -3x - 7
Both equations are the same, indicating that the two lines are the same line and have many solutions.