The image shows two linear equations:

1. $y = 3x - 5$
2. $y = 3x + 2$

These are equations of lines in slope-intercept form, $y = mx + b$, where:

• $m$ (the coefficient of $x$) is the slope.
• $b$ is the y-intercept.

Analysis of Each Equation

• For $y = 3x - 5$:

  • Slope ($m$) = 3
  • Y-intercept ($b$) = -5

• For $y = 3x + 2$:

  • Slope ($m$) = 3
  • Y-intercept ($b$) = 2

Observations

Both lines have the same slope of 3, meaning they are parallel. However, they have different y-intercepts, so they will never intersect. Parallel lines have no points in common, and thus there is no solution if we're trying to find an intersection point.

Would you like a detailed explanation on how to graph these lines or explore further properties?

Related Questions

1. How do we find the distance between two parallel lines?
2. How would the equations change if the slopes were different?
3. What would happen if we added a system with a third equation?
4. How can we determine if lines are perpendicular?
5. How do we write equations for lines that intersect at a specific point?

Tip:

In a system of linear equations, if the lines are parallel, they have no solution (they are inconsistent).