How to turn point slope into slope intercept?
Understand the Problem
The question is asking how to convert a linear equation from point-slope form to slope-intercept form. The point-slope form is usually represented as y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. To convert this to the slope-intercept form (y = mx + b), one would solve for y.
Answer
$y = mx + (y_1 - mx_1)$
Answer for screen readers
The equation in slope-intercept form is $y = mx + (y_1 - mx_1)$.
Steps to Solve
- Identify the values in the point-slope form
Start with the point-slope form equation: $$ y - y_1 = m(x - x_1) $$
Identify the slope $m$ and the point $(x_1, y_1)$ from the equation.
- Distribute the slope
Distribute the slope across the term $(x - x_1)$: $$ y - y_1 = mx - mx_1 $$
- Isolate y
To isolate $y$, add $y_1$ to both sides of the equation: $$ y = mx - mx_1 + y_1 $$
- Rewrite in slope-intercept form
Now, consolidate the constants: $$ y = mx + (y_1 - mx_1) $$
Here, the term $(y_1 - mx_1)$ represents the y-intercept $b$. Thus, the equation is now in slope-intercept form: $$ y = mx + b $$
The equation in slope-intercept form is $y = mx + (y_1 - mx_1)$.
More Information
This transformation allows you to easily identify the slope and the y-intercept of the line. The slope-intercept form is particularly useful for graphing linear equations.
Tips
- Forgetting to distribute the slope properly may lead to incorrect terms in the equation.
- Neglecting to combine like terms effectively when isolating $y$ can create errors in the final equation.
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