Let's solve the equation step by step:

You provided:

\[
y = 2x \cdot 1 + 5
\]

### Step 1: Simplify the multiplication
First, simplify the term \( 2x \cdot 1 \):

\[
y = 2x + 5
\]

### Step 2: Interpret the equation
Now, we have the equation in its simplified form:

\[
y = 2x + 5
\]

This is a linear equation in slope-intercept form \( y = mx + b \), where:
- \( m = 2 \) (slope of the line)
- \( b = 5 \) (y-intercept, which means the line crosses the y-axis at \( y = 5 \))

This equation represents a straight line where, for each value of \( x \), the corresponding value of \( y \) can be found by substituting \( x \) into the equation.

### Step 3: Example calculations
Let's plug in a few values for \( x \) to see what the corresponding \( y \)-values are:

- If \( x = 0 \):

\[
y = 2(0) + 5 = 5
\]

- If \( x = 1 \):

\[
y = 2(1) + 5 = 7
\]

- If \( x = -1 \):

\[
y = 2(-1) + 5 = 3
\]

The line goes through the points \( (0, 5) \), \( (1, 7) \), and \( (-1, 3) \).

Would you like more details on how to plot or analyze this linear function? 

Here are 5 related questions:
1. What is the slope and its significance in a linear equation?
2. How do you find the x-intercept of this line?
3. What happens if the slope changes to another value?
4. How do you solve for \( x \) given a specific \( y \)-value?
5. How does this equation relate to the general form \( ax + by = c \)?

**Tip:** In linear equations, the slope determines how steep the line is, while the y-intercept determines where the line crosses the y-axis.

Explore how to solve the linear equation y = 2x + 5 with detailed steps. This lesson covers key algebraic concepts such as slope-intercept form, how to find the slope and y-intercept, and example calculations. Suitable for students in Grades 6-8.

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