How to write standard form with two points?
Understand the Problem
The question is asking how to write the equation of a line in standard form given two points that lie on the line. To solve this, we first need to calculate the slope of the line using the two points, and then use the point-slope form to convert it into standard form.
Answer
The standard form of the line is $Ax + By = C$.
Answer for screen readers
The standard form of the equation of the line is $Ax + By = C$.
Steps to Solve
- Calculate the Slope
To find the slope $m$ of the line that passes through the points $(x_1, y_1)$ and $(x_2, y_2)$, we use the formula:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
- Use Point-Slope Form
Once we have the slope, we can use one of the points (let's say $(x_1, y_1)$) to write the equation of the line in point-slope form:
$$ y - y_1 = m(x - x_1) $$
- Rearrange to Standard Form
To convert the point-slope equation to standard form ($Ax + By = C$), we will rearrange the equation:
- Move all terms involving $x$ and $y$ to one side of the equation and the constant to the other side.
- Simplify the Equation
Ensure that $A$, $B$, and $C$ are integers, and $A$ is non-negative. If necessary, multiply through by any common denominators to eliminate fractions.
The standard form of the equation of the line is $Ax + By = C$.
More Information
The standard form of the equation of a line is useful in various applications, including graphing linear equations and solving systems of equations. Its format allows for easy identification of the intercepts and relationships between variables.
Tips
- Forgetting to calculate the slope correctly.
- Not rearranging all terms properly into the standard form.
- Misplacing a negative sign during simplification.
