What is the exact solution to the system of equations shown on the graph?
A diagonal curve declines through (negative 1 point 2, negative 4 point 8), and (2, negative 5). A diagonal curve rises from (negative 6, negative 5) and (negative 4, negative 1). Both curves intersect at (negative 1 point 2, negative 4 point 8).
The system of equations can be written as:
y = mx + b1 (equation for the declining diagonal curve)
y = mx + b2 (equation for the rising diagonal curve)
We need to find the values of m, b1, and b2.
From the given points (−1.2,−4.8) and (2,−5), we can find the slope (m1) for the declining diagonal curve:
m1 = (−5−(−4.8))/(2−(−1.2)) = −0.2/3.2 = −0.0625
Using the point-slope form with the point (−1.2,−4.8) and the slope m1, we can determine b1:
y − (−4.8) = −0.0625(x − (−1.2))
y + 4.8 = −0.0625(x + 1.2)
y + 4.8 = −0.0625x − 0.075
y = −0.0625x − 4.875
Similarly, from the given points (−6,−5) and (−4,−1), we can find the slope (m2) for the rising diagonal curve:
m2 = (−1−(−5))/((−4)−(−6)) = 4/2 = 2
Using the point-slope form with the point (−6,−5) and the slope m2, we can determine b2:
y − (−5) = 2(x − (−6))
y + 5 = 2(x + 6)
y + 5 = 2x + 12
y = 2x + 7
Therefore, the exact solution to the system of equations is:
y = −0.0625x − 4.875 (equation for the declining diagonal curve)
y = 2x + 7 (equation for the rising diagonal curve)