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Rewrite each equation in slope-intercept form 3x + 5y = 12 2. 5x – 4y = 6

User Meeka
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Final answer:

The given equations 3x + 5y = 12 and 5x – 4y = 6 have been rewritten in slope-intercept form as y = (-3/5)x + 12/5 and y = (5/4)x - 3/2, respectively, showing their slopes and y-intercepts.

Step-by-step explanation:

To rewrite the equation 3x + 5y = 12 in slope-intercept form, we need to solve for y to get it into the form y = mx + b, where m represents the slope and b represents the y-intercept. Here's the process:

  • 3x + 5y = 12
  • Subtract 3x from both sides: 5y = -3x + 12
  • Divide every term by 5: y = (-3/5)x + 12/5

Now, the equation is in slope-intercept form with a slope of -3/5 and a y-intercept of 12/5.

Next, for the equation 5x – 4y = 6:

  • 5x - 4y = 6
  • Subtract 5x from both sides: -4y = -5x + 6
  • Divide every term by -4: y = (5/4)x - 6/4
  • Simplify the y-intercept: y = (5/4)x - 3/2

Now, the equation is in slope-intercept form with a slope of 5/4 and a y-intercept of -3/2.

User Nick Louloudakis
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