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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?

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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


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 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

  • m represents the slope of the line

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


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.

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?

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:

  • 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:

  • 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:

  • 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


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