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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.

Give the equation that has the indicated characteristics: a zero at 1, and a slope of 2. Enter the correct equation in the box.

Learn how to derive the equation of a line with a zero at 1 and a slope of 2. This problem explores key concepts in algebra and linear equations, using the slope-intercept form y = mx + b. Suitable for students in Grades 8-10.

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