Question

choose the best graph that represents the linear equation: -2x - 16y = -8 graph a graph of a coordinate plane with a line graph b graph of a coordinate plane, partial

Explanation:

Answer:

To determine the correct graph, we first rewrite the linear equation \(-2x - 16y = -8\) in slope - intercept form (\(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept).

Step 1: Isolate \(y\)

Start with the given equation:

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The slope \(m =-\frac{1}{8}\) (a small negative slope) and the y - intercept \(b=\frac{1}{2}\) (the line crosses the y - axis at \(y = 0.5\)).

Step 2: Analyze the graphs

• For a line with a slope of \(-\frac{1}{8}\), it is a very gentle (shallow) negative slope. The y - intercept is positive (\(y=\frac{1}{2}\)).
• Graph A: Looking at the general shape, if we assume that the line in Graph A has a shallow negative slope and crosses the y - axis near \(y = 0.5\) (since the y - intercept is \(\frac{1}{2}\)), it is consistent with the equation \(y =-\frac{1}{8}x+\frac{1}{2}\).
• Since Graph B's details are not fully visible, but from the equation's properties (shallow negative slope, positive y - intercept), Graph A is the best representation.

So the answer is Graph A.