What are the charateristics of the graph of the line:  y = 1/3 x – 9    

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of the line to be graphed and its characteristics determined is y = (1/3)x - 9

This is in the form y = mx + c, where m is the slope of the line and c is the y-intercept.

As y = (1/3)x - 9, the slope of the given line is (1/3). The y-intercept is (0, -9).

The x-intercept can be found by solving the equation (1/3)x - 9 = 0.

This gives x = 9*3 = 27. The x-intercept is (27, 0)

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The form of the equation of the line you,ve provided is the slope intercept form.

y = mx + b, where m is the slope of the line and b is y intercept, we'll get:

Comparing both forms:

m = 1/3 and y = -9

Now, we'll determine the intrcepting point of the line with x and y axis.

When the line is intercepting x axis, y coordinate is 0.

x/3 - 9 = 0

x/3 = 9

x = 27

The intrercepting point with x axis is: (27,0).

The intercepting point with y axis is (0,-9).

Therefore, the characteristics of the given line are the intercepting points with x and y axis and the angle made by the line to x axis, which may be found when we know the value of the slope: x axis intercept (27,0) ; y axis intercept (0,-9) and the slope m=1/3.

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