Standard Form Slope Intercept Form Calculator Using Points

Linear Equation Forms:

\[ \text{Standard Form: } Ax + By = C \] \[ \text{Slope-Intercept Form: } y = mx + b \]

Slope-Intercept Form:

Standard Form:

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1. What Are Standard and Slope-Intercept Forms?

The slope-intercept form (y = mx + b) directly shows the slope (m) and y-intercept (b) of a line. The standard form (Ax + By = C) is often used for systems of equations and has integer coefficients when possible.

2. How Does the Calculator Work?

The calculator uses two points to first find the slope (m), then the y-intercept (b):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \] \[ b = y_1 - m \times x_1 \]

Then converts between forms:

Slope-Intercept: y = mx + b
Standard Form: mx - y = b (simplified to integer coefficients)

3. Importance of Linear Equations

Details: Linear equations are fundamental in algebra and appear in various applications from physics to economics. Understanding different forms helps in graphing and solving systems of equations.

4. Using the Calculator

Tips: Enter any two distinct points on a line. The calculator will provide both forms of the equation. Vertical lines (undefined slope) will show an error.

5. Frequently Asked Questions (FAQ)

Q1: What if my line is vertical?
A: Vertical lines (x = a) have undefined slope and cannot be expressed in slope-intercept form. The calculator will show an error.

Q2: What if my line is horizontal?
A: Horizontal lines (y = b) have slope 0 and work normally (e.g., y = 0x + b).

Q3: Why does standard form sometimes have different coefficients?
A: The calculator simplifies to the smallest integer coefficients. For exact decimal values, use slope-intercept form.

Q4: Can I use fractions as input?
A: Yes, but enter them as decimals (e.g., 0.5 for 1/2). The calculator handles decimal inputs.

Q5: How accurate are the results?
A: Results are accurate to 2 decimal places. For exact fractional forms, manual calculation may be needed.