The equation given in the image is:

$x - y = 3$

To rewrite this equation in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, follow these steps:

Steps:

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

2. Subtract $x$ from both sides to isolate $-y$: $-y = -x + 3$

3. Multiply through by $-1$ to make $y$ positive: $y = x - 3$

Final Answer:

$y = x - 3$

This is the slope-intercept form. Here:

• The slope ($m$) is $1$.
• The y-intercept ($b$) is $-3$.

Do you have any questions or want further details? Here are related follow-up questions:

1. How do you find the slope and y-intercept directly from an equation in slope-intercept form?
2. What does the slope of $m = 1$ mean for the graph of this equation?
3. How would the graph of this equation look like? (E.g., the line passes through $(0, -3)$.)
4. How can you convert other forms of equations (e.g., standard form) into slope-intercept form?
5. What are some practical uses of slope-intercept form in real-life problems?

Tip:

Always isolate $y$ on one side of the equation to convert into slope-intercept form!