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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Lines and Equations

⇒ We have built tables and plotted points for equations in the standard form: Ax + By = C or the slope-intercept form: y = m x + b and noted that (a , 0), or (x0 , 0), is the x-intercept and (0, b), or (0, y0), is the y-intercept.

⇒ Now let us explore another equation given the slope-intercept form: y = m x + b:

where m is the slope and b (0 , b) is the y-intercept: y = mx + b.

Example.

Graph the linear equation 3x - 2y = 6 or

Compare this equation to the given the slope-intercept form: y = m x + b:

⇒ Write the slope and the y-intercept b = - 6 or (0, b) = (0, - 6 ).

Use the fact that the slope is to find dx = 2 and dy = 3

Now, build a table using the common differences. On the table put the point where x = 0 in the middle of the x-sequence, add dx to get the next value below, and complete the x-sequence. Look at the given table and see how it is started. Since both columns must be arithmetic sequences use the value for dy and add it to b in the point (0, b) to complete the table and plot the points.

Build the table and plot the points: 3x - 2y = 6

 x y -4 -9 dx = 2 -2 -6 dy = 3 0 -3 2 0 4 3

Check the a point (6, 6) not on your table by replacing x and y in the given equation.

3x - 2y = 6 → 3(6) - 2(6) = 6