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The problem presents the equation \( y = 2x \) and asks to graph it, passing through the origin, and to determine the coordinates of the point when \( x = -3 \).

### Step 1: Understand the equation
The equation \( y = 2x \) is a straight line in slope-intercept form, where:
- The slope \( k = 2 \), meaning for every unit increase in \( x \), \( y \) increases by 2 units.
- The y-intercept is 0, meaning the line passes through the origin \( (0, 0) \).

### Step 2: Find a second point
You're asked to determine a second point by letting \( x = -3 \).

- Substitute \( x = -3 \) into the equation \( y = 2x \):
  \[
  y = 2(-3) = -6
  \]
So, the point \( (-3, -6) \) is on the line.

### Step 3: Plotting the points
The line passes through the origin \( (0, 0) \) and the point \( (-3, -6) \). You can plot these two points and draw a straight line through them to represent the equation \( y = 2x \).

Do you want further details or have any questions?

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Here are five related questions:
1. What is the slope of the line \( y = 2x \) and how does it affect the graph's steepness?
2. If \( x = 4 \), what would \( y \) be according to the equation \( y = 2x \)?
3. How do you find the y-intercept of a linear equation in slope-intercept form?
4. Can the equation \( y = 2x \) be expressed in a different form, such as point-slope form?
5. How does the graph of \( y = 2x \) compare to that of \( y = -2x \)?

**Tip**: To graph a line efficiently, it's helpful to plot the y-intercept and at least one additional point based on the slope.

An equation of the form y = kx, where k is a real number, k ≠ 0, will always pass through the origin. Determine a second point. Use this information to graph the line of the following equation: y = 2x. Let x = -3. Plot (x, y).

Learn how to graph the equation y = 2x and plot the point when x = -3. This problem involves basic linear equations, determining the slope, and plotting points on a graph. Suitable for students in Grades 6-8.

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