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The slope-intercept form of a line: y = mx + b PowerPoint PPT Presentation


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The slope-intercept form of a line: y = mx + b. 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 = mx+b form. What does m represent in each equation? - PowerPoint PPT Presentation

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

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The slope intercept form of a line y mx b l.jpg

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


Graph the following family of lines using the graphing calculator l.jpg

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 = mx+b form. What does m represent in each equation?

    Check your hypothesis by using the table feature of the calculator.


Graph the following family of lines using the graphing calculator3 l.jpg

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 = mx+b form. What does b represent in each equation?

    Check your hypothesis by using the table feature of the calculator.


Given y mx b l.jpg

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.


Slide5 l.jpg

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


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

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 y–intercept of 4 and slope 2/3.

  • that is horizontal and passes through the point ( 2, 5)


What if the equation is not given in y mx b form l.jpg

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.


To find the x intercept and the y intercept of a line written in standard form l.jpg

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.


Graphing equations in different forms l.jpg

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.


Assignment l.jpg

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