The equation you provided is in slope-intercept form, which is expressed as:

$y = mx + b$

where:

• $m$ is the slope of the line (rate of change).
• $b$ is the y-intercept (the value of $y$ when $x = 0$).

For the equation $y = 3x - 1$:

• The slope $m = 3$. This means for every unit increase in $x$, $y$ increases by 3.
• The y-intercept $b = -1$. This means the line crosses the y-axis at $y = -1$.

Properties of this equation:

1. Slope: 3 (The line rises steeply).
2. Y-intercept: -1 (Where the line crosses the y-axis).
3. X-intercept: To find the x-intercept, set $y = 0$ and solve for $x$: $0 = 3x - 1 \implies 3x = 1 \implies x = \frac{1}{3}$

This line has a positive slope, meaning it is increasing from left to right.

Would you like more details, or do you have any specific questions?

Related questions:

1. What does the slope of 3 tell us about the behavior of the line?
2. How do we graph the line based on its slope and intercept?
3. What happens to the line if the slope changes to a negative number?
4. Can you rewrite the equation in standard form $Ax + By = C$?
5. What is the significance of the x-intercept?

Tip:

When graphing a line from its equation, always start by plotting the y-intercept, then use the slope to find additional points.