How do I write 2x + 5y = 10 in slope-intercept form?

To convert the equation 2x + 5y = 10 into slope-intercept form, we need to find the value of y in terms of x. The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Here are the steps to rearrange the equation:

1. Start with the original equation: 2x + 5y = 10.
2. Subtract 2x from both sides to isolate the 5y term:
3. 5y = -2x + 10
4. Next, divide every term by 5 to solve for y:
5. y = -rac{2}{5}x + 2

Now, we have the equation in slope-intercept form. Here, the slope m is -2/5 and the y-intercept b is 2. This means the line descends at a rate of 2 units down for every 5 units it moves to the right, and it crosses the y-axis at 2.