To solve for $m$ (the slope) and $b$ (the y-intercept) in each equation, let's rewrite each in the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Problem (1)

Given: $y = 4x - 10$ This equation is already in slope-intercept form $y = mx + b$.

• Slope (m): $m = 4$
• Y-intercept (b): $b = -10$

Problem (2)

Given: $4 - 10x = y$ Rearrange to match $y = mx + b$: $y = -10x + 4$

• Slope (m): $m = -10$
• Y-intercept (b): $b = 4$

Summary:

1. Equation (1): $y = 4x - 10$

   • $m = 4$
   • $b = -10$

2. Equation (2): $y = -10x + 4$

   • $m = -10$
   • $b = 4$

Would you like more details or have any questions?

Related Questions:

1. How do we find the slope from two points on a line?
2. What are the different forms of a linear equation?
3. How do we convert an equation from standard form to slope-intercept form?
4. How can we determine if two lines are parallel?
5. How can we find the x-intercept of a line?

Tip:

Always try to rearrange equations into slope-intercept form $y = mx + b$ to quickly identify the slope and y-intercept.