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 Amsco Integrated Algebra I: Graphing Linear Functions Using Their Slopes
This is a free lesson from our course in Amsco's Integrated Algebra
 
   
In this lesson you’ll learn the basic concepts of graphing linear functions using their slopes; with the help of several examples, video and in own hand wring by the instructor. Linear function means: linear equation with two variables. The slope and any one point can be used to draw the graph of a linear function. The simplest way to graph a linear function is - find two points on the line, plot these points on the coordinate plane and connect the points with a line. (More text below video...)
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(Continued from above) For example: to draw graph of the function 2x + 3y = 9, follow the below given steps:
• transform the equation into the form: y = -2/3 x + 3
• find the slope of the line slope i.e. the coefficient of x: -2/3
• find the y-intercept of the y-intercept i.e. 3
• on the y-axis, graph point A, with its y-coordinate as the y-intercept:
• use the slope to find two more points on the line i.e. B and C and locate them
• draw the line that passes through the three points:
This line is the graph of 2x + 3y = 9.

Further you’ll learn an alternative way of looking at the effects of changing the values of the y-intercept and slope i.e. translating, reflecting, or scaling the graph of the linear function y = x. E.g. the graph of y = x + 3 can be thought of as the graph of y = x shifted 3 units up. Remember the following rules:
• Translation rules for linear functions, if c is positive:
The graph of y = x + c is the graph of y = x shifted c units up.
The graph of y = x - c is the graph of y = x shifted c units down.
• Reflection rule for linear functions:
The graph of y = -x is the graph of y = x reflected in the x-axis.
• Scaling rules for linear functions:
When c > 1, the graph of y = cx is the graph of y = x stretched vertically by a factor of c.
When 0 < c < 1, the graph of y = cx is the graph of y = x compressed vertically by a factor of c.
The video above explains more details on Graphing Linear Functions using their Slopes, with the help of several examples and their solutions.
 
   

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