The equation $y = 4x + 2$ represents a linear equation in two variables, $x$ and $y$. Here's the breakdown and explanation:

1. General Form of a Linear Equation

The equation $y = 4x + 2$ is in slope-intercept form: $y = mx + b$ where:

• $m$ is the slope of the line.
• $b$ is the y-intercept, the value of $y$ when $x = 0$.

2. Slope ($m$)

In this equation, the slope ($m$) is 4. This means:

• For every unit increase in $x$, $y$ increases by 4.
• The slope represents the steepness of the line.

3. Y-Intercept ($b$)

The y-intercept ($b$) is 2. This is the point where the line crosses the $y$-axis. The coordinates of this point are $(0, 2)$.

4. Graph of the Equation

The graph of $y = 4x + 2$ is a straight line that:

1. Passes through $(0, 2)$ (the y-intercept).
2. Has a slope of 4, so it rises by 4 units vertically for every 1 unit it moves horizontally.

Example Points on the Line:

To plot the line, substitute different $x$-values into the equation:

• If $x = 0$: $y = 4(0) + 2 = 2$ → Point: $(0, 2)$.
• If $x = 1$: $y = 4(1) + 2 = 6$ → Point: $(1, 6)$.
• If $x = -1$: $y = 4(-1) + 2 = -2$ → Point: $(-1, -2)$.

Visual Interpretation:

The line goes through points like $(0, 2), (1, 6), (-1, -2)$ and extends infinitely in both directions. Its steep slope reflects that $y$ changes rapidly with $x$.

Would you like a graph or further clarification?

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Here are 5 related questions you might explore:

1. What is the equation of a line parallel to $y = 4x + 2$?
2. How do you find the slope of a line from two points?
3. How do you determine if a point lies on the line $y = 4x + 2$?
4. What is the equation of a line perpendicular to $y = 4x + 2$?
5. How would you write $y = 4x + 2$ in standard form?

Tip: Always check the slope ($m$) and y-intercept ($b$) to quickly understand the behavior of a line!