To write the equation $5x + 2y = 10$ in slope-intercept form ($y = mx + b$, where $m$ is the slope and $b$ is the y-intercept), we need to solve for $y$.

Step-by-step process:

1. Start with the given equation: $5x + 2y = 10$

2. Subtract $5x$ from both sides to isolate the $y$ term: $2y = -5x + 10$

3. Divide both sides of the equation by 2 to solve for $y$: $y = \frac{-5x + 10}{2}$

4. Simplify the right-hand side: $y = -\frac{5}{2}x + 5$

Slope-Intercept Form:

The equation is now in slope-intercept form: $y = -\frac{5}{2}x + 5$

• Slope ($m$): $-\frac{5}{2}$
• Y-intercept ($b$): $5$

Conclusion

The slope of the line is $-\frac{5}{2}$, and the y-intercept is $5$.

Would you like more details or have any questions?

Related Questions:

1. How would you convert $3x + 4y = 12$ into slope-intercept form?
2. What is the slope of the equation $2x + y = 8$?
3. How do you find the x-intercept and y-intercept of a line from its equation?
4. Can you explain how to graph the line $y = -\frac{5}{2}x + 5$?
5. How do you convert the equation $x = 4$ into slope-intercept form?

Tip:

To convert an equation into slope-intercept form, focus on isolating $y$ on one side. Once $y$ is by itself, the coefficient of $x$ gives you the slope, and the constant term is the y-intercept.