Lesson Graphing and Slope of a Line

Source code of 'Graphing and Slope of a Line'

This Lesson (Graphing and Slope of a Line) was created by by rapaljer(4671)

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About rapaljer: Retired Professor of Mathematics from Seminole State College of Florida after 36 years.

Whenever the equation of a line is given in the form y =mx+b, which is called the slope-intercept form, the line is easily graphed in the following way.

General explanation of y =mx+b.  The y-intercept of a graph is the point where x=0.  In the general equation y=mx+b, when x=0, the y-intercept is the constant coefficient (that it, the number term of the equation.)  The steepness or slope of the line is the coefficient of x, which in this case is m.  The slope is actually the rise over the run, the vertical distance divided by the horizontal distance from one point to another point on the line.  With these two (the Y-intercept and the slope!) it is really easy to draw a graph.

EXAMPLES:

y=1*x+2
The y-intercept is the number term which is 2, and the slope is the coefficient of x, which is 1.

To draw the graph, go up two units on the y axis and put a point.  Then, because the slope is 1, which means 1 over 1, with your pencil on this point go up another 1 and go right 1 and put another point.  Connect these two points, and it should look like this:

{{{graph ( 300,300, -10, 10, -10, 10, x+2)}}}

y=-1*x+2
The y-intercept is the number term which is 2, and the slope is the coefficient of x, which is -1.

To draw the graph, go up two units on the y axis and put a point.  Then, because the slope is -1, which means -1 over 1, with your pencil on this point go down another 1 and go right 1 and put another point.  Connect these two points, and it should look like this:

{{{graph ( 300,300, -10, 10, -10, 10, -x+2)}}}

{{{y=(3/5)*x+3}}}
The y-intercept is the number term which is 3, and the slope is the coefficient of x, which is {{{3/5}}}.

To draw the graph, go up three units on the y axis and put a point.  Then, because the slope is {{{3/5}}}, with your pencil on this point go up 3 and go right 5 and put another point.  Connect these two points, and it should look like this:

{{{graph ( 300,300, -10, 10, -10, 10, (3/5)*x+3)}}}

{{{y=(-3/5)*x+3}}}
The y-intercept is the number term which is 3, and the slope is the coefficient of x, which is {{{-3/5}}}.

To draw the graph, go up three units on the y axis and put a point.  Then, because the slope is {{{-3/5}}}, with your pencil on this point go down 3 and go right 5 and put another point.  Connect these two points, and it should look like this:

{{{graph ( 300,300, -10, 10, -10, 10, (-3/5)*x+3)}}}

R^2  Retired