In the image, you are asked to match each linear equation to its corresponding graph. The equations are:

1. $y = -7x - 2$
2. $y = 7x + 2$
3. $y = -7x + 2$
4. $y = 7x - 2$

The graphs (A, B, C, and D) show various straight lines, which you must match to the equations. To do this, focus on the slope (steepness of the line) and the y-intercept (where the line crosses the y-axis) in each equation.

Let's break it down:

• Equation 1: $y = -7x - 2$

  • Slope $m = -7$ (negative, steep)
  • Y-intercept: $-2$

• Equation 2: $y = 7x + 2$

  • Slope $m = 7$ (positive, steep)
  • Y-intercept: $2$

• Equation 3: $y = -7x + 2$

  • Slope $m = -7$ (negative, steep)
  • Y-intercept: $2$

• Equation 4: $y = 7x - 2$

  • Slope $m = 7$ (positive, steep)
  • Y-intercept: $-2$

Now look at the graphs:

• If the line slopes upwards, it has a positive slope.
• If the line slopes downwards, it has a negative slope.
• Look at the point where the line crosses the y-axis for the intercept.

This will help you match each equation to the correct graph.

Would you like me to give you the final match-up, or do you prefer solving this yourself?

Here are 5 related questions to deepen understanding:

1. What does the slope of a line represent in a graph?
2. How do you find the y-intercept from a linear equation?
3. What happens to the graph if the slope of a line is zero?
4. How can you determine if two lines are parallel just by looking at their equations?
5. What is the geometric meaning of a negative slope?

Tip: The y-intercept helps you quickly identify where the line crosses the y-axis, making graph matching easier!