# 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

• 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

More Examples

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

• What is the y-intercept of the line given by the equation below?
• y = -6x + 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?