The equation $y = 5x + 1$ represents a linear function. Here's a breakdown of the equation:

1. Slope (m): The coefficient of $x$, which is 5, represents the slope of the line. It indicates that for every unit increase in $x$, $y$ increases by 5 units.

2. Y-intercept (b): The constant term, which is 1, represents the y-intercept. This is the point where the line crosses the y-axis ($x = 0$).

3. Graph: The graph of this equation would be a straight line with a slope of 5, and it would cross the y-axis at the point (0, 1).

Key Points

• If $x = 0$, then $y = 1$.
• If $x = 1$, then $y = 6$.
• The slope of 5 indicates a steep incline.

Would you like further details on how to graph this or how to solve for $x$ or $y$ in a specific scenario?

Related Questions

1. What is the slope-intercept form of a linear equation?
2. How do you graph the line $y = 5x + 1$?
3. What is the effect of changing the slope on the graph of a line?
4. How can you find the x-intercept of the equation $y = 5x + 1$?
5. What happens to the graph if the y-intercept is changed?

Tip: When solving or graphing linear equations, identifying the slope and y-intercept helps you quickly sketch the graph.