Writing the equation of a line
Understand the Problem
The question is asking how to write the equation of a line, which typically involves finding the slope and y-intercept or using a specific point and slope to form the equation. This is a fundamental concept in algebra that allows us to represent linear relationships mathematically.
Answer
The equation of the line is $y = mx + b$.
Answer for screen readers
The equation of the line can be written as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
Steps to Solve
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Identify the Slope and Y-Intercept To write the equation of the line in the slope-intercept form, which is $y = mx + b$, we need to know the slope ($m$) and the y-intercept ($b$). Look for given values or points that might indicate these.
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Use the Point-Slope Formula If we have a specific point $(x_1, y_1)$ and the slope $m$, we can use the point-slope formula: $$ y - y_1 = m(x - x_1) $$ This helps us write the equation in a different form, which can then be converted to slope-intercept form.
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Rearranging the Equation After applying the point-slope formula, rearrange the equation to the slope-intercept form $y = mx + b$. Add or subtract terms as necessary to isolate $y$.
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Final Equation Representation Once in the slope-intercept form, identify the final values for $m$ (slope) and $b$ (y-intercept) to present the equation fully as $y = mx + b$.
The equation of the line can be written as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
More Information
Understanding how to derive the equation of a line is crucial in algebra. This process helps with graphing linear functions, solving systems of equations, and many real-world applications such as financial modeling and physics.
Tips
- Confusing the slope with the y-intercept: Ensure you identify both values correctly when using points or drawing graphs.
- Neglecting to simplify the equation properly when rearranging: Always double-check arithmetic when moving terms from one side of the equation to the other.
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