How can the expression 3x + 5y + 10 = 0 be rewritten in slope-intercept form?

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To convert the equation 3x + 5y + 10 = 0 into slope-intercept form, which is typically written as y = mx + b (where m is the slope and b is the y-intercept), we need to isolate y on one side of the equation.

Here’s a step-by-step breakdown:

  1. Start with the original equation: 
    3x + 5y + 10 = 0
  2. Subtract 3x and 10 from both sides: 
    5y = -3x - 10
  3. Now, to isolate y, divide every term by 5: 
    y = -rac{3}{5}x - 2

Now the equation is in slope-intercept form, where:

  • The slope (m) is -3/5
  • The y-intercept (b) is -2

Thus, the expression 3x + 5y + 10 = 0 written in slope-intercept form is:

y = -3/5x – 2

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