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.