The slope-intercept form of a line: y = mx b

1
The slope-intercept form of a liney mx b

2
Graph the following family of lines using the
graphing calculator

• y 3x 2
• y 5x 2
• y -4 x 2
• y 1/2 x 2
• All of these equations are written in
• y mxb form. What does m represent in each
  equation?
• Check your hypothesis by using the table feature
  of the calculator.

3
Graph the following family of lines using the
graphing calculator

• y 3x 2
• y 3x - 4
• y 3x
• y 3 x 8
• All of these equations are written in
• y mxb form. What does b represent in each
  equation?
• Check your hypothesis by using the table feature
  of the calculator.

4
Given y mx b

• m represents the slope of the line
• b represents the y-intercept -- the point where
  the line intercepts or crosses the y-axis.

5
Graphing lines in the form y mx b is very
easy since you know one point, the y-intercept,
and the slope.

• Graph each of the following
• y 2x 5
• y - x 3
• y 4x
• y - 2

6
Finding the equations of lines is very easy if
you know the y-intercept and slope.

• Find the equation of the line
• that passes through the origin with slope 2.
• with yintercept of 4 and slope 2/3.
• that is horizontal and passes through the point (
  2, 5)

7
What if the equation is not given in y mx b
form?

• Graph the equation whose standard form is 3x 2y
  6.
• Strategy 1 Rewrite the equation in y
  mx b form.
• Strategy 2 Find the x-intercept and the
  y-intercept.

8
To find the x-intercept and the y-intercept of a
line written in standard form

• Let x 0 to find the y-intercept.
• Let y 0 to find the x-intercept.
• Example Find the x-intercept and the
  y-intercept of the line 3x 5y 15. Then graph
  the line.

9
Graphing equations in different forms

• Point-slope form y y1 m(x x1)
• Use a point (x1, y1 ) and the slope, m.
• Standard form Ax By C
• Rewrite in y mx b form OR
• Find the x-intercept and the y-intercept OR
• Make a table of solutions.
• Slope-intercept form y mx b
• Use the y-intercept and the slope.

10
Assignment

• 6.4 19-45 odds
• Due Wednesday 1/14/04
• 6.5 13-25 all. Use graph paper. Write the
  equation next to each graph.
• Due Thursday 1/15/05