To derive the equation of a line in slope-intercept form \(y = mx + b\), we need to identify the slope \(m\) and the y-intercept \(b\) from the graph of the line. Since the graph is not provided directly, I can't analyze it, but I can explain how to do this step-by-step.
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Identify two points on the line: Look for clear points where the line intersects the grid. It’s best to select points with whole number coordinates for accuracy.
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Calculate the slope: Use the formula for slope: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \((x_1, y_1)\) and \((x_2, y_2)\) are the two points you identified.
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Find the y-intercept: Locate the point where the line crosses the y-axis. This point has coordinates in the form \((0, b)\), where \(b\) is the y-intercept.
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Write the equation: Plug the slope and the y-intercept into the slope-intercept form \(y = mx + b\).
If we assume you're provided with four potential line equations:
- \(y = -3x - 4\)
- \(3x - y = 4\) (which can be converted to slope-intercept form)
- \(y = 3x - 4\)
- \(y = 3x + 4\)
You can look for the line that has the same slope and y-intercept as the calculations yield from your graph analysis.
Without the specific graph, I can't definitively tell you which equation is correct. However, if you identify the slope and intercept correctly from the graph, you will be able to match it to one of the options provided.
3 answers