To derive the equation of the line in slope-intercept form (y = mx + b), we will analyze the options given, as they seem to represent different lines.
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Slope-Intercept Form:
- The form \(y = mx + b\) indicates that \(m\) is the slope and \(b\) is the y-intercept.
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Given Options:
- Option 1: \(y = 3x - 4\) (Slope = 3, Y-intercept = -4)
- Option 2: \(y = -3x - 4\) (Slope = -3, Y-intercept = -4)
- Option 3: \(y = 3x + 4\) (Slope = 3, Y-intercept = 4)
- Option 4: \(3x - y = 4\) which can be rearranged to \(y = 3x - 4\) (Slope = 3, Y-intercept = -4)
From the options, we see that the first and fourth equations provide the same line:
- Using the Fourth Equation: To rearrange \(3x - y = 4\) into slope-intercept form: \[ -y = -3x + 4 \] \[ y = 3x - 4 \]
Depending on where the line crosses the y-axis and its slope (visualized on the graph), we would consider the correct lines based on the graph that corresponds to the presented options.
The final equation in slope-intercept form derived from the context provided is:
\[ y = 3x - 4 \]
If you have specific coordinate points or a visual to reference, please provide them for a more accurate analysis.