Let's work through the problem step by step.

Given Equation:

$4x - 7y = 28$

(a) Write it in slope-intercept form ($y = mx + b$):

To convert the equation into slope-intercept form, we need to solve for $y$.

$4x - 7y = 28$

Subtract $4x$ from both sides:

$-7y = -4x + 28$

Now, divide every term by $-7$ to solve for $y$:

$y = \frac{4}{7}x - 4$

So, the equation in slope-intercept form is:

$y = \frac{4}{7}x - 4$

(b) Slope of the line:

In the slope-intercept form $y = mx + b$, the coefficient of $x$ is the slope $m$.

So, the slope $m$ is:

$\text{slope} = \frac{4}{7}$

(c) Y-intercept:

The y-intercept $b$ is the constant term in the slope-intercept form.

Here, the y-intercept is:

$\text{y-intercept} = -4$

(d) Graph the line:

To graph the line, you can plot the y-intercept $(0, -4)$ and then use the slope $\frac{4}{7}$ to find another point. Starting from $(0, -4)$, you move up 4 units and to the right 7 units to plot the next point.

Would you like me to generate the graph for you?

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If you have any questions or want further details, feel free to ask! Here are 5 related questions for you to consider:

1. How do you determine the slope from two points on a line?
2. What does the slope of a line represent geometrically?
3. How do you find the x-intercept of a line?
4. What happens to the graph of a line if the slope is negative?
5. How can you check if a point lies on a given line?

Tip: When converting an equation to slope-intercept form, always isolate the $y$ term by dividing or multiplying as necessary.