Let's solve the equations step by step to convert them from standard form $Ax + By = C$ to slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. $4x + 6y = 48$

Steps:

1. Subtract $4x$ from both sides: $6y = -4x + 48$
2. Divide every term by $6$ to solve for $y$: $y = -\frac{4}{6}x + \frac{48}{6}$
3. Simplify fractions: $y = -\frac{2}{3}x + 8$

Answer: $y = -\frac{2}{3}x + 8$

2. $3x - 5y = 25$

Steps:

1. Subtract $3x$ from both sides: $-5y = -3x + 25$
2. Divide every term by $-5$ to solve for $y$: $y = \frac{-3}{-5}x + \frac{25}{-5}$
3. Simplify fractions: $y = \frac{3}{5}x - 5$

Answer: $y = \frac{3}{5}x - 5$

Would you like further clarification or additional examples?

5 Related Questions:

1. What is the significance of the slope in slope-intercept form?
2. How do you determine the y-intercept in these equations?
3. Can you graph $y = -\frac{2}{3}x + 8$ and $y = \frac{3}{5}x - 5$?
4. How does converting to slope-intercept form help with graphing?
5. What are some real-world applications of linear equations in slope-intercept form?

Tip:

To quickly find the slope from the standard form $Ax + By = C$, use $m = -\frac{A}{B}$.