The equation \( y = 1 + 2x \) is a linear equation in two variables, \(x\) and \(y\). It represents a straight line when plotted on a coordinate plane.

### Breakdown:
- **Slope**: The coefficient of \(x\), which is \(2\), is the slope of the line. This means for every unit increase in \(x\), \(y\) increases by 2 units.
- **Y-intercept**: The constant term \(1\) is the y-intercept. This means the line crosses the y-axis at \(y = 1\).

### Example:
If \(x = 0\), then:
\[
y = 1 + 2(0) = 1
\]
If \(x = 1\), then:
\[
y = 1 + 2(1) = 3
\]

So, two points on the line would be \((0, 1)\) and \((1, 3)\).

Would you like to see the graph of this line or a more detailed explanation?

### 5 Related Questions:
1. What does the slope represent in a linear equation?
2. How do you calculate the slope between two points on a line?
3. How can you write the equation of a line given its slope and one point?
4. How do you solve for \(x\) in \(y = 1 + 2x\) if a specific \(y\) value is given?
5. What is the general form of a linear equation?

**Tip**: When analyzing linear equations, always identify the slope and y-intercept to understand how the line behaves.

Explore the linear equation y = 1 + 2x and learn how to calculate its slope and y-intercept. This step-by-step explanation covers key algebraic concepts, such as the slope-intercept form of a line, and is suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation