How do I write the equation 5x + 2y = 10 in the form y = mx + b?

To rewrite the equation 5x + 2y = 10 in the slope-intercept form, which is y = mx + b, we need to isolate y on one side of the equation.

Here are the steps to follow:

1. Start with the original equation: 5x + 2y = 10.
2. Subtract 5x from both sides to get 2y by itself: 2y = 10 – 5x.
3. To isolate y, divide each term in the equation by 2: y = rac{10}{2} – rac{5x}{2}.
4. This simplifies to: y = 5 – rac{5}{2}x.

Now, our equation is in the form of y = mx + b, where:

• m, the slope, is -rac{5}{2}
• b, the y-intercept, is 5

So, the final rewritten equation is: y = -rac{5}{2}x + 5.