Question

the equations \\(9x - 10y = 6\\), \\(8x - 10y = -23\\), \\(9x + 10y = -16\\), and \\(8x + 10y = 13\\) are shown on the graph below.

Explanation:

Convert equations to slope-intercept form

Using the Slope-Intercept Form knowledge point

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Match lines to the graph

Using the Linear Equation Graphing knowledge point

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Identify intersections

Using the Line Intersection knowledge point

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Answer:

The four equations correspond to the colored lines on the graph as follows:

• Green line: \(8x - 10y = -23\) (slope \(m = 0.8\), y-intercept \(b = 2.3\))
• Pink line: \(9x - 10y = 6\) (slope \(m = 0.9\), y-intercept \(b = -0.6\))
• Blue line: \(8x + 10y = 13\) (slope \(m = -0.8\), y-intercept \(b = 1.3\))
• Teal line: \(9x + 10y = -16\) (slope \(m = -0.9\), y-intercept \(b = -1.6\))