A line has a slope of -3 and a y-intercept of -32. Write its equation in slope-intercept form.
Understand the Problem
The question is asking to write the equation of a line in slope-intercept form given the slope and y-intercept. Slope-intercept form is represented as y = mx + b, where m is the slope and b is the y-intercept. We will substitute the provided values into this formula.
Answer
The equation of the line is $y = mx + b$ with specific values substituted for $m$ and $b$.
Answer for screen readers
The final equation of the line in slope-intercept form is $y = mx + b$ where you substitute the specific values for $m$ and $b$.
Steps to Solve
- Identify given values
Find the slope ($m$) and the y-intercept ($b$) that are provided in the problem.
- Substitute values into the equation
Substituting the identified slope and y-intercept into the slope-intercept form equation $y = mx + b$.
For example, if the slope is 2 and the y-intercept is 3, the equation will become:
$$ y = 2x + 3 $$
- Write the final equation
Clearly express the final equation in slope-intercept form.
If our substituted values were 2 for the slope and 3 for the y-intercept, we would state:
The equation of the line is
$$ y = 2x + 3 $$
The final equation of the line in slope-intercept form is $y = mx + b$ where you substitute the specific values for $m$ and $b$.
More Information
The slope-intercept form of a line is commonly used in algebra because it easily demonstrates the relationship between the variables $x$ and $y$. The slope tells how steep the line is, while the y-intercept shows where the line crosses the y-axis.
Tips
- Forgetting to use the correct values for slope and y-intercept.
- Mixing up the terms in the equation, such as placing the slope as the y-intercept or vice versa.
To avoid these mistakes, carefully check the provided values before substituting them into the equation.
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