To solve for $y$ in the equation $4x - 3y = 4$, follow these steps:

1. Solve for $y$:

Start with the given equation: $4x - 3y = 4$

1. Subtract $4x$ from both sides to isolate the $y$ term: $-3y = 4 - 4x$

2. Divide both sides of the equation by $-3$ to solve for $y$: $y = \frac{4 - 4x}{-3}$ Simplifying further: $y = \frac{-4x + 4}{-3} \quad \text{or} \quad y = \frac{4x - 4}{3}$

Thus, the equation solved for $y$ is: $y = \frac{4x - 4}{3}$

2. Graph the Equation:

To graph this linear equation, note that it is in the slope-intercept form $y = mx + b$, where:

• Slope ($m$) = $\frac{4}{3}$
• y-intercept ($b$) = $-\frac{4}{3}$

Using a standard window on a graphing utility (e.g., $x$ and $y$ values ranging from $-10$ to $10$):

1. y-intercept: The graph will cross the $y$-axis at $-\frac{4}{3}$ (or approximately $-1.33$).
2. Slope: From the y-intercept, go up 4 units and to the right 3 units to plot the next point, as the slope is $\frac{4}{3}$.

Would you like me to generate a visual graph for you?

Here are five related questions:

1. How do you find the x-intercept of the equation $4x - 3y = 4$?
2. What does the slope $\frac{4}{3}$ indicate about the steepness and direction of the line?
3. How would the graph change if the equation were $4x - 3y = 10$?
4. How can you rewrite the equation in point-slope form?
5. How do parallel and perpendicular lines relate to the given equation?

Tip: When graphing a line, finding both intercepts (x and y) can help quickly sketch the graph without needing to plot multiple points.