The graph you described represents a system of two linear equations.
Let's denote the two lines based on their intercepts:
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The first line, which has a positive slope and crosses the x-axis at \((-8, 0)\) and the y-axis at \((0, 8)\), can be expressed in slope-intercept form \(y = mx + b\). The slope \(m\) can be calculated as follows:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 0}{0 - (-8)} = \frac{8}{8} = 1 \]
The equation of the first line is:
\[ y = 1x + 8 \Rightarrow y = x + 8 \]
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The second line, which has a negative slope and crosses the x-axis at \((-2, 0)\) and the y-axis at \((0, -2)\), also can be expressed in slope-intercept form. The slope \(m\) is calculated as follows:
\[ m = \frac{-2 - 0}{0 - (-2)} = \frac{-2}{2} = -1 \]
The equation of the second line is:
\[ y = -1x - 2 \Rightarrow y = -x - 2 \]
Now, the system of equations can be represented as:
\[ \begin{align*} 1.\quad y &= x + 8 \ 2.\quad y &= -x - 2 \end{align*} \]
To find the solution of this system, we substitute \(y\) from the first equation into the second equation:
\[ x + 8 = -x - 2 \]
Now, solve for \(x\):
\[ x + x = -2 - 8 \] \[ 2x = -10 \] \[ x = -5 \]
Now substitute \(x = -5\) back into the first equation to find \(y\):
\[ y = -5 + 8 = 3 \]
Thus, the solution of this system of equations is:
\[ \boxed{(-5, 3)} \]
This confirms that the lines intersect at the coordinate \((-5, 3)\), which is the solution to the system.
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