Question

give examples of a slope-intercept form, standard form, and point-slope form

Answer 1

Certainly! Let's look at the different forms of linear equations: slope-intercept form, standard form, and point-slope form.

### 1. Slope-Intercept Form
The slope-intercept form of a linear equation is given by:
\[ y = mx + b \]
where \( m \) is the slope, and \( b \) is the y-intercept.

**Example:**
\[ y = 2x + 3 \]
- Here, the slope \( m = 2 \) and the y-intercept \( b = 3 \).

### 2. Standard Form
The standard form of a linear equation is given by:
\[ Ax + By = C \]
where \( A \), \( B \), and \( C \) are integers, and \( A \) should be non-negative.

**Example:**
\[ 2x + 3y = 6 \]
- In this equation, \( A = 2 \), \( B = 3 \), and \( C = 6 \).

### 3. Point-Slope Form
The point-slope form of a linear equation is given by:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is a specific point on the line, and \( m \) is the slope.

**Example:**
\[ y - 4 = -1(x - 2) \]
- Here, the slope \( m = -1 \), and the point \( (x_1, y_1) = (2, 4) \).

These three forms are often used to represent linear equations in different contexts and can be converted from one to another as needed!