Find the equation of a line given the slope and y-intercept.
Understand the Problem
The question is asking for the equation of a line, given its slope and y-intercept. The equation of a line in slope-intercept form is typically written as y = mx + b, where m represents the slope and b stands for the y-intercept.
Answer
The equation of the line is $$ y = 2x - 3 $$.
Answer for screen readers
The equation of the line is $$ y = 2x - 3 $$.
Steps to Solve
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Identify the slope and y-intercept Firstly, determine the values for the slope ($m$) and the y-intercept ($b$) from the problem statement. For example, if it's given that the slope is 2 and the y-intercept is -3, we can write: $$ m = 2 $$ $$ b = -3 $$
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Write the equation of the line Use the slope-intercept form of the equation of a line, which is $$ y = mx + b $$ Substituting the identified values of $m$ and $b$ into this equation gives: $$ y = 2x - 3 $$
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Final form of the equation Ensure that your equation is in the correct format. Check for any simplifications if necessary, but in this case, the equation is already in its simplest form. The final equation is: $$ y = 2x - 3 $$
The equation of the line is $$ y = 2x - 3 $$.
More Information
The slope-intercept form is a pivotal concept in algebra and helps in visualizing and graphing linear equations. The slope indicates the steepness of the line, and the y-intercept indicates where the line crosses the y-axis.
Tips
- Mixing up slope and y-intercept: Ensure to clearly identify which value corresponds to $m$ (slope) and $b$ (y-intercept) from the problem statement.
- Incorrect substitution: Double-check that the values are substituted correctly into the equation format.
