Forms of the Equation of a Straight Line
A line can be written in slope-intercept, point-slope, two-point, intercept or normal form, each equivalent to ax + by + c = 0.
What is Forms of the Equation of a Straight Line?
A line can be written in slope-intercept, point-slope, two-point, intercept or normal form, each equivalent to ax + by + c = 0.
Key formula / rule: Slope-intercept y = mx + c fails for vertical lines.
Key points
- Derive the equation of a line from given geometric data.
- Compute the angle between two lines from their slopes.
Common exam trap
Missing the vertical-line case when working with slopes.
Definitions
- Term
Forms of the Equation of a Straight Line
- Meaning
A line can be written in slope-intercept, point-slope, two-point, intercept or normal form, each equivalent to ax + by + c = 0.
- Term
Forms of the Equation of a Straight Line — explanation
- Meaning
Choosing the form that matches the given data avoids algebra. Slope is undefined for vertical lines, which is the source of most missed cases.
Learning objectives
Derive the equation of a line from given geometric data.
Compute the angle between two lines from their slopes.
Formulae
- Key point
Slope-intercept y = mx + c fails for vertical lines.
- Key point
Two lines are parallel when slopes are equal and perpendicular when the product of slopes is -1.
- Key point
General form ax + by + c = 0 covers every line including vertical ones.
Common mistakes
Missing the vertical-line case when working with slopes.
Mixing intercept form with slope form coefficients.
Keywords
Forms
Equation
Straight
Line
Practice preview
Which of the following statements about the equation of a straight line is INCORRECT?…
hard
What is the slope-intercept form of the equation of a straight line?…
easy
Find the equation of a straight line with a slope of 3 and a y-intercept of -2.…
easy