SlopeIntercept Form of the Equation of a Line

1
Slope-Intercept Form of the Equation of a Line

• The line with slope m and y-intercept (0,b) has
  equation
• y m x b.
• Example 2.  Find the slope and y-intercept of
  the line 3x 4y - 5 0.
• When we solve the equation above for y, we get
• y (-3/4)x 5/4,
• Which is the Slope-Intercept form of the
  equation.
• The slope of the line is the coefficient of x,
  -3/4.
• The y-intercept is the point (0,5/4).

2
Point-Slope Form of an Equation of a Line

• y - y1 m(x - x1)
• m being the slope
• y1 being the y-coordinate of the known point
• x1 being the x-coordinate of the same known point

3
Horizontal Lines

• All points on a horizontal line have the same
  y-coordinate, and the x-coordinate can be any
  number.
• The equation of a line spells out the conditions
  that the coordinates of a point must satisfy to
  be on the line. In the case of a horizontal line,
  there is no restriction on the x-coordinate, so x
  doesn't appear in the equation.
• The condition on the y-coordinate is that it
  must equal a fixed number, so the equation of a
  horizontal line has the form y b, where b is a
  number.

4
Vertical Lines

• All points on a vertical line have the same
  x-coordinate, and the y-coordinate can be any
  number. Therefore, the equation of a vertical
  line has the form x a, where a is a number.

5
Slope Formula
Given any two points (x1, y1) and (x2, y2) on a
line, the slope, m, of the line is given by
This formula might be easier to remember if you
think of it as "Rise over Run." "Rise" is the
vertical change, or change in the y coordinate as
you move from point 1 to point 2, and "Run" is
the horizontal change. Note that rise or run can
be negative numbers.
6
Example 4

• Joe is a sales clerk in a department store and
  his gross pay for the month is determined by the
  value of the merchandise that he sells that
  month. One month he had 12000 in sales and his
  gross pay was 1960. The next month he had only
  9000 in sales and his gross pay fell to 1720.

7
Example 4

• Write a linear equation giving Joe's gross pay y
  in terms of his monthly sales amount x.
• We know two points on the graph of the equation
  (12000,1960) and (9000,1720).
• The slope of the line is m (1960-1720)/(12000-90
  00) 0.08.

8
Example 4

• Using the second point (9000,1720) and the slope
  m 0.08 we find the Point-Slope form of the
  equation of the line to be
• y - 1720 0.08 (x - 9000).
• Solving for y yields the Slope-Intercept form
• y 0.08 x 1000.