Equations of Straight Lines Topic Index | Algebra Index | Regents Exam Prep Center

When working with straight lines, there are several ways to arrive at an equation which represents the line.

 Remember: Slope is found by using the formula: Slope is also expressed as rise/run.

Equation Forms of Straight Lines

 Slope Intercept Form Point Slope Form Use this form when you know the slope and the y-intercept (where the line crosses the y-axis). y = mx + b m = slope b = y-intercept  (where line crosses the y-axis.) Use this form when you know a point on the line and the slope (or can determine the slope). m = slope = any point on the line

 Horizontal Lines Vertical Lines y = 3 (or any number) Lines that are horizontal have a slope of zero.  Horizontal lines have "run", but no "rise".   The rise/run formula for slope always yields zero since the rise = 0. Since the slope is zero, we have y = mx + b y = 0•x + 3 y = 3 This equation also describes what is happening to the y-coordinates on the line.  In this case the y-coordinates are always 3. x = -2 (or any number) Lines that are vertical have no slope (it does not exist).  Vertical lines have "rise", but no "run".  The rise/run formula for slope always has a zero denominator and is undefined. The equations for these lines describe what is happening to the x-coordinates.  In this example, the x-coordinates are always equal to -2.

Examples:

 Examples using Slope-Intercept Form: Examples using Point-Slope Form: 1.  Find the slope and y-intercept for the equation 2y = -6x + 8. First solve for "y =":      y = -3x + 4 Remember the form:     y = mx + b Answer:  the slope (m) is -3                 the y-intercept (b) is 4 3.  Given that the slope of a line is -3 and the line passes through the point (-2,4), write the equation of the line.  The slope:  m = -3 The point (x1 ,y1) = (-2,4) Remember the form:  y - y1 = m ( x - x1) Substitute:                 y - 4 = -3 (x - (-2)) ANS.                        y - 4 = -3 ( x + 2)   If asked to express the answer in "y =" form:             y - 4 = -3x - 6                           y = -3x - 2 2.  Find the equation of the line whose slope is 4 and the coordinates of the y-intercept are (0,2). In this problem m = 4 and b = 2. Remember the form:  y = mx + b and that b is where the line crosses the y-axis. Substitute:           y = 4x + 2 4.  Find the slope of the line that passes through the points (-3,5) and (-5,-8). First, find the slope:    Use either point:  (-3,5) Remember the form:  y - y1 = m ( x - x1) Substitute:  y - 5 = 6.5 ( x - (-3))                   y - 5 = 6.5 (x + 3)  Ans.

 Topic Index | Algebra Index | Regents Exam Prep Center Created by Donna Roberts