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If a line has the equation 7x + 2y = 14, what is the slope of the line? (2023)

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Question: If a line has the equation 7x + 2y = 14, what is the slope of the line? (2023)

Options:

  1. -7/2
  2. 7/2
  3. 2/7
  4. -2/7

Correct Answer: -7/2

Exam Year: 2023

Solution: 

Rearranging to slope-intercept form gives y = -7/2x + 7, so the slope is -7/2.

If a line has the equation 7x + 2y = 14, what is the slope of the line? (2023)

Practice Questions

Q1
If a line has the equation 7x + 2y = 14, what is the slope of the line? (2023)
  1. -7/2
  2. 7/2
  3. 2/7
  4. -2/7

Questions & Step-by-Step Solutions

If a line has the equation 7x + 2y = 14, what is the slope of the line? (2023)
  • Step 1: Start with the equation of the line: 7x + 2y = 14.
  • Step 2: To find the slope, we need to rearrange this equation into slope-intercept form, which is y = mx + b, where m is the slope.
  • Step 3: First, isolate the term with y. Subtract 7x from both sides: 2y = -7x + 14.
  • Step 4: Now, divide every term by 2 to solve for y: y = (-7/2)x + 14/2.
  • Step 5: Simplify 14/2 to get 7: y = (-7/2)x + 7.
  • Step 6: Now, we can see that the slope (m) is -7/2.
  • Slope-Intercept Form – Understanding how to rearrange a linear equation into the form y = mx + b, where m represents the slope.
  • Linear Equations – Recognizing the standard form of a linear equation and how to manipulate it to find the slope.
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