Question

115 \\(3x - 2y = 4\\)

Explanation:

Convert to slope-intercept form

Using the Slope-Intercept Form knowledge point

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Identify slope and y-intercept

Using the Slope-Intercept Form knowledge point

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Find a second point

Using the Graphing Linear Equations knowledge point

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Draw the line

Using the Graphing Linear Equations knowledge point

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Answer:

To graph the linear equation \(3x - 2y = 4\), we first rewrite it in slope-intercept form \(y = mx + b\):

$$y = \frac{3}{2}x - 2$$

From this equation, we identify:

• The \(y\)-intercept is at \((0, -2)\).
• The slope \(m = \frac{3}{2}\), which means we go up \(3\) units and right \(2\) units to find a second point at \((2, 1)\).

Drawing a straight line through \((0, -2)\) and \((2, 1)\) gives the graph of the equation.