We are asked to find an equation that satisfies the following conditions:

• The independent variable is $x$, and the dependent variable is $y$.
• The equation has a zero at $x = 1$ (which means $y = 0$ when $x = 1$).
• The slope of the line is 2.

This describes a linear equation in slope-intercept form, $y = mx + b$, where:

• $m$ is the slope.
• $b$ is the y-intercept.

Step 1: Apply the slope

The slope is given as $2$, so we start with the equation: $y = 2x + b$

Step 2: Use the zero condition

We know that the equation has a zero at $x = 1$, meaning $y = 0$ when $x = 1$. Substitute $x = 1$ and $y = 0$ into the equation: $0 = 2(1) + b$ $0 = 2 + b$ Solving for $b$, we get: $b = -2$

Final Equation

Thus, the equation is: $y = 2x - 2$

Would you like more details on this solution? Here are some follow-up questions:

1. What is the general form of a linear equation, and how is it different from the slope-intercept form?
2. How can you check if the solution is correct by plugging in different values for $x$?
3. How does the slope affect the steepness of the line?
4. What are other forms of linear equations besides slope-intercept form?
5. How would the equation change if the slope was negative instead of positive?

Tip: When solving for linear equations, always use the slope and a known point to quickly find the y-intercept.