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4.3 – Slope-Intercept Equation of a Line

Key Terms

  • Y-axis – The vertical axis in a Cartesian coordinate system.
  • Y-intercept – A point where the graph of a function crosses the y-axis.
    • A function has at most one y-intercept.
    • The y-intercept of the line with equation y = mx + b is the point (0, b).
    • The x coordinate is zero for each line’s y-intercept.
  • Slope-Intercept Equation – One way to write the equation of a line.
    • It is shown as y = mx + b, where m is the slope and b is the y-coordinate of the line’s y-intercept.

 

Review

  • Slope – Steepness of a line
    • Slope = Rise / Run
    • The slope measures the rate of change (subtraction) of they-variable with respect to the x-variable, written as:
      • \frac{y_2-y_1}{x_2-x_1}
    • Slope is represented in linear equations by the letter “m,” which is the coefficient of the x-variable
      • The slope of the line is the coefficient of the variable x in the equation y = mx + b

 

Notes

  • Slope-Intercept Equation of a Line

Alg1B 4.3 Slope Intercept Form Labeled Alg1B 4.3 Slope Intercept Form

 


  • The y-intercept
    • Where the line crosses the y-axis
    • Written as (0,b), where 0 is the x-coordinate and b is the y-coordinate

 


  • Slope-Intercept Example

Alg1B 4.3 Slope Intercept Ex

 

More Examples

  • What is the slope of the line given by the equation below?
    • y = -17x + 5
    • Answer: -17

 

  • What is the y-intercept of the line given by the equation below?
    • y = -6x + 9
    • Answer: (0,9)

 

  • If the y-intercept of a line is (0,-2) and the slope is 6, what is the slope-intercept equation of the line?
    • Answer: y = 6x – 2

 

  • In the slope-intercept equation of a line, which part of the equation gives the slope of the line?
    • Answer: The coefficient of the x-term

 

  • In the slope-intercept equation of a line, which part of the equation gives the y-coordinate of the point where the line crosses the y-axis?
    • Answer: The constant term

 


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