Point-Slope Form to Slope-Intercept Form Calculator

Point-Slope to Slope-Intercept Conversion:

\[ y = m x + (y_1 - m x_1) \]

Slope (m):

unitless

X-coordinate of Point (x₁):

unitless

Y-coordinate of Point (y₁):

unitless

Slope-Intercept Form:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Point-Slope to Slope-Intercept Conversion?

The conversion from point-slope form (y - y₁ = m(x - x₁)) to slope-intercept form (y = mx + b) is a fundamental algebraic process that transforms a linear equation from one representation to another while maintaining the same line graph.

2. How Does the Calculator Work?

The calculator uses the conversion formula:

\[ y = m x + (y_1 - m x_1) \]

Where:

\( m \) — Slope of the line (unitless)
\( x_1 \) — X-coordinate of the given point (unitless)
\( y_1 \) — Y-coordinate of the given point (unitless)
\( y_1 - m x_1 \) — Y-intercept (b) of the line (unitless)

Explanation: The formula rearranges the point-slope form by solving for y and simplifying to obtain the slope-intercept form y = mx + b.

3. Importance of Form Conversion

Details: Converting between different forms of linear equations is essential for graphing, solving systems of equations, and understanding the relationship between slope, intercepts, and points on a line.

4. Using the Calculator

Tips: Enter the slope (m) and coordinates of a point (x₁, y₁) on the line. The calculator will automatically convert the point-slope form to slope-intercept form.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between point-slope and slope-intercept forms?
A: Point-slope form emphasizes a specific point on the line, while slope-intercept form highlights the slope and y-intercept of the line.

Q2: When should I use point-slope form?
A: Use point-slope form when you know a point on the line and the slope, particularly useful for writing equations quickly.

Q3: When is slope-intercept form more useful?
A: Slope-intercept form is ideal for graphing and quickly identifying the slope and y-intercept of a line.

Q4: Can I convert from slope-intercept to point-slope form?
A: Yes, by selecting any point on the line (often the y-intercept is convenient) and using the slope.

Q5: What if my slope is zero or undefined?
A: For zero slope (horizontal line), the equation becomes y = b. For undefined slope (vertical line), the equation is x = constant, which cannot be expressed in slope-intercept form.