To graph the equation $y = 4x + 2$, follow these steps:

1. Understand the Equation:

• The equation $y = 4x + 2$ is in slope-intercept form: $y = mx + b$.
• $m = 4$: This is the slope, indicating the rate of change or the steepness of the line.
• $b = 2$: This is the y-intercept, the point where the line crosses the y-axis.

2. Plot the Y-Intercept:

• Start by plotting the y-intercept ($b$) on the y-axis. For this equation, $b = 2$, so plot the point $(0, 2)$.

3. Use the Slope to Find Another Point:

• The slope $m = 4$ can be written as $\frac{4}{1}$, meaning "rise over run."
• From the y-intercept $(0, 2)$, move up 4 units (rise) and right 1 unit (run) to locate another point, $(1, 6)$.

4. Plot the Second Point:

• Place a point at $(1, 6)$ on the graph.

5. Draw the Line:

• Use a ruler to connect the two points $(0, 2)$ and $(1, 6)$ with a straight line. Extend the line in both directions.

6. Label the Line:

• Add the equation $y = 4x + 2$ near the line for clarity.

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Key Features:

• Slope: The line is steep because the slope is large ($m = 4$).
• Y-Intercept: The line crosses the y-axis at $(0, 2)$.

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Would you like me to provide a visual graph of this equation? Let me know!

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Related Questions:

1. What does the slope $m = 4$ mean in practical terms?
2. How would you graph the equation if the slope were negative?
3. How do you convert $y = 4x + 2$ into standard form?
4. What happens to the graph if you change the y-intercept $b$?
5. How would you graph $y = 4x - 3$ compared to $y = 4x + 2$?

Tip:

Always double-check your slope calculation by confirming the rise/run between points!