5x+2y=10 the slope intercept of the equation is

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.

5x + 2y = 10 the slope intercept of the equation is

Learn how to convert the linear equation 5x + 2y = 10 into slope-intercept form with a detailed step-by-step explanation. This problem covers key algebra concepts, including isolating y and identifying the slope and y-intercept. Suitable for students in Grades 8-10.

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