The equation $y = 7x - 2$ represents a linear function. Let's analyze its components:

Key Features:

1. Slope (m): The coefficient of $x$ is 7, which means the slope of the line is 7. This tells us that for every 1 unit increase in $x$, $y$ will increase by 7 units.
2. Y-intercept (b): The constant term is -2, which means the line crosses the y-axis at $(0, -2)$.
3. Graph: Since the slope is positive, the line will slant upwards from left to right.

General Form:

The equation is in the slope-intercept form: $y = mx + b$ where:

• $m = 7$ (slope)
• $b = -2$ (y-intercept)

Example:

If you want to find the value of $y$ for $x = 3$, you can substitute: $y = 7(3) - 2 = 21 - 2 = 19$ So, when $x = 3$, $y = 19$.

Would you like more details or have any specific questions?

Related Questions:

1. How would the graph change if the slope were negative?
2. What are the coordinates of the x-intercept for this line?
3. Can you write the equation in standard form?
4. How do you determine the slope from a graph?
5. What is the significance of the slope and y-intercept in a real-world scenario?

Tip:

When analyzing linear equations, always look at the slope to understand the rate of change and the y-intercept to know where the line crosses the y-axis.