What is the slope of the line represented by the equation 2x + 4y = 10?

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To find the slope of the line given by the equation 2x + 4y = 10, we first need to rearrange this equation into the form y = mx + b, where m represents the slope and b represents the y-intercept.

Start by isolating y. We can do this by following these steps:

  1. Subtract 2x from both sides of the equation:

    2. 4y = 10 – 2x

  2. Next, divide every term by 4 to solve for y:

    3. y = - rac{1}{2}x + rac{5}{2}

Now, the equation is in slope-intercept form. Here, we can see that the slope m is - rac{1}{2}. This means the slope of the line is negative, indicating that as x increases, y decreases.

To summarize, the slope of the line represented by the equation 2x + 4y = 10 is - rac{1}{2}.

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