- 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.
- 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:
- 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
- Slope-Intercept Equation of a Line
- 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
- 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