The equation provided is a linear equation in two variables, $3x - y = 4$. To work with it, let's explore the solutions and possible interpretations:

Solving for $y$ in terms of $x$

To express $y$ in terms of $x$, we can isolate $y$ on one side of the equation:

$3x - y = 4$

Subtract $3x$ from both sides:

$-y = -3x + 4$

Now, multiply both sides by -1 to solve for $y$:

$y = 3x - 4$

So, the equation in slope-intercept form is:

$y = 3x - 4$

Interpretation

1. The slope of this line is $3$, indicating it rises by 3 units for every unit it moves to the right.
2. The y-intercept of the line is $-4$, meaning it crosses the y-axis at $(0, -4)$.

Example Points on the Line

To plot this line, let's substitute a few values for $x$ and calculate $y$:

• If $x = 0$: $y = 3(0) - 4 = -4$ (point $(0, -4)$)
• If $x = 1$: $y = 3(1) - 4 = -1$ (point $(1, -1)$)
• If $x = 2$: $y = 3(2) - 4 = 2$ (point $(2, 2)$)

Would you like further steps or details? Here are five related questions you might explore:

1. How do I graph this equation on a coordinate plane?
2. What is the x-intercept of this line?
3. How do we find the distance between two points on this line?
4. What is the general approach to solving for $y$ in terms of $x$?
5. Can we solve this equation with a second equation to find an intersection point?

Tip: When converting equations to slope-intercept form, aim to isolate $y$ to easily identify the slope and intercept.