Questions: Solve the system of functions by graphing. Then classify the system. f(x) = -1/6 x - 5 g(x) = 1/6 x - 7 Use the graphing tool to graph the system.

Solution Steps

The given system of functions is: \[ f(x) = -\frac{1}{6}x - 5 \] \[ g(x) = -\frac{1}{6}x - 7 \]

Both functions have the same slope of \(-\frac{1}{6}\), but different y-intercepts:

• For \( f(x) \), the y-intercept is \(-5\).
• For \( g(x) \), the y-intercept is \(-7\).

1. Graph \( f(x) = -\frac{1}{6}x - 5 \):

   • Start at the y-intercept \((0, -5)\).
   • Use the slope \(-\frac{1}{6}\) to find another point. For example, from \((0, -5)\), move 1 unit to the right and \(\frac{1}{6}\) unit down to get the point \((6, -6)\).

2. Graph \( g(x) = -\frac{1}{6}x - 7 \):

   • Start at the y-intercept \((0, -7)\).
   • Use the slope \(-\frac{1}{6}\) to find another point. For example, from \((0, -7)\), move 1 unit to the right and \(\frac{1}{6}\) unit down to get the point \((6, -8)\).

Since both lines have the same slope but different y-intercepts, they are parallel and will never intersect.

Final Answer