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Find the equation of the line that passes through the origin and has a slope of

Practice Questions

Q1
Find the equation of the line that passes through the origin and has a slope of -3.
  1. y = -3x
  2. y = 3x
  3. y = -x/3
  4. y = 1/3x

Questions & Step-by-Step Solutions

Find the equation of the line that passes through the origin and has a slope of -3.
  • Step 1: Understand that the equation of a line can be written in the slope-intercept form, which is y = mx + b.
  • Step 2: Identify the slope (m) given in the question. Here, the slope is -3.
  • Step 3: Since the line passes through the origin, the y-intercept (b) is 0.
  • Step 4: Substitute the slope and y-intercept into the slope-intercept form: y = -3x + 0.
  • Step 5: Simplify the equation. Since +0 does not change the equation, it becomes y = -3x.
  • Slope-Intercept Form – The equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.
  • Understanding Slope – The slope indicates the steepness and direction of the line; a negative slope means the line descends from left to right.
  • Intercepts – The line passes through the origin, meaning the y-intercept (b) is 0.
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