Download Algebra I 4-6 notes October 31, 2016

Algebra I 4-6 notes
4.6, Model Direct Variation
Today we will...
- Write direct variation equations.
- Graph direct variation equations.
October 31, 2016
Two variables x and y show direct variation provided y = ax and a ≠ 0.
The nonzero number a is called the constant of variation, and y is said
to vary directly with x.
The equation y = 5x is an example of direct variation, and the constant of
variation is 5. The equation y = x + 5 is NOT an example of direct
variation.
Tell whether the equation represents direct variation. If so, identify the
constant of variation.
-x + y = 1
Tell whether the equation represents direct variation. If so, identify the
constant of variation.
2x + y = 0
Tell whether the equation represents direct variation. If so, identify the
constant of variation.
4x - 5y = 0
Algebra I 4-6 notes
October 31, 2016
Direct Variation Graphs
Notice that a direct variation equation, y = ax, is a linear equation in
slope-intercept form, y = mx + b, with m = a and b= 0. The graph of a
direct variation equation is a line with a slope of a and a y-intercept of 0.
So, the line passes through the origin.
Graph the direct variation equation.
y= 2 x
5
Graph the direct variation equation.
y = - 1x
2
Graph the direct variation equation y = 2x.
Algebra I 4-6 notes
The graph of a direct variation equation passes through the point (4, 6).
Write the direct variation equation and find the value of y when x = 24.
October 31, 2016
The graph of a direct variation equation is shown.
Write the direct variation equation.
Find the value of y when x = 14.
An object that weighs 100 pounds on Earth would weigh just 6 pounds on
Pluto. Assume that weight P on Pluto varies directly with weight E on
Earth.
Write a direct variation equation that relates P and E.
What would a boulder weighing 750 pounds on Earth weigh on Pluto?
Ratios
y
The direct variation equation y = ax can be written as x = a for x ≠ 0. So,
in a direct variation, the ratio of y to x is the constant for all nonzero data
pairs (x, y).
Given that y varies directly with x, use the specified values to write a
direct variation equation that relates x and y.
x = 24, y = 3
Algebra I 4-6 notes
Given that y varies directly with x, use the specified values to write a
direct variation equation that relates x and y.
x = -16, y = -4
The table shows the cost of buying used DVDs at a music store.
Explain why C varies directly with d.
Write a direct variation equation that relates d and C.
October 31, 2016
Given that y varies directly with x, use the specified values to write a
direct variation equation that relates x and y.
x = 8, y = -3