Let's solve the given equation of the line, $4x - 3y = -3$, to find the slope and y-intercept.

We start by converting the equation to slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Solve for $y$

We have: $4x - 3y = -3$ Subtract $4x$ from both sides: $-3y = -4x - 3$ Now, divide both sides by $-3$: $y = \frac{4}{3}x + 1$

Step 2: Identify the slope and y-intercept

• The slope $m = \frac{4}{3}$
• The y-intercept $b = 1$

Now that we have the slope and y-intercept, you can use these values to graph the line on the provided graph.

Would you like further details or have any questions?

Here are some related questions to deepen your understanding:

1. How can you graph a line using the slope and y-intercept?
2. What does the slope of a line represent geometrically?
3. How would the graph change if the slope were negative?
4. What is the effect of changing the y-intercept on the graph of a line?
5. How would you convert an equation from standard form to point-slope form?

Tip: When graphing, start by plotting the y-intercept, then use the slope to find another point on the line.