Direct & Partial Variation Ryan Duffy

Direct Variation A relationship between two variables in which one variable is a constant multiple of the other. When graphing the line DOES pass through the origin. Represented by y=mx form X and Y values vary directly with each other

Partial Variation A relationship between two variables in which one variable is a constant multiple of the other plus a constant value. Graph DOES NOT pass through the origin. Represented by y=mx+b form

y=mx & y=mx+b Mean? What does... *y=mx and y=mx+b *Y is the unknown value *M is the slope or how much the line increases *B is the Y-intercept *X is the value on the X-axis

y=mx & y=mx+b Direct Variation Partial Variation y=mx M: is the constant of variation y=mx+b M: is the constant of variation B: is the fixed cost

Direct Variation Partial Variation straight line constant of variation no fixed cost fixed cost x and y values starts at origin starts anywhere but origin y=mx y=mx+b

Examples

Examples For Direct Variation Bubba earns 24.00$ per hour at his grandfathers donkey farm. Create a table of values that displays the money earned by Bubba in 6 hours. Example #1 Hours Money Earned 1 24.00 2 48.00 3 72.00 4 96.00 5 120.00 6 144.00 Not real graph (example)

Therefore this is in the form of y=mx, so it is a Direct Variation The relation for Bubba's graph displays the relationship between his hours worked and his wages. We can say that his wages vary directly with the hours worked. This type of relation is known as a direct variation. If we examine the formula of his hours worked and his wages, we would get y=24x Therefore this is in the form of y=mx, so it is a Direct Variation

Examples for Partial Variation Bubba gets a new job at his uncles lama farm. He now gets paid 9.00$ a day plus 27.00$ per hour create a table of values that displays the money Bubba earns at his new job. Hours Money Earned 9.00 1 36.00 2 63.00 3 90.00 4 117.00 5 144.00 6 171.00 Not real graph ( Example)

Therefore this is in the form of y=mx+b, which is a Partial Variation The relation for Bubba's graph displays the new relationship between his hours worked and his wages with a fixed daily wage. We can say that his wages vary partially with the hours worked. This type of relation is known as a partial variation. If we examine the formula of his hours worked and his wages, we would get y=27x+9 Therefore this is in the form of y=mx+b, which is a Partial Variation

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