Answer:
The direct variation says that: [tex]y \propto x[/tex]
Then the equation is of the form:
[tex]y=kx[/tex] where k is the constant of Variation.
As per the statement:
A number b varies directly with the number a.
i.e [tex]b \propto a[/tex]
By definition of direct variation:
[tex]b = ka[/tex] Â Â Â Â Â Â Â .....[1]
if [tex]b= 2\frac{3}{4}[/tex] and [tex]a=-2\frac{3}{4}[/tex]
Substitute in [1] we get k;
[tex]2\frac{3}{4}= k(- 2\frac{3}{4})[/tex]
Divide both sides by [tex]2\frac{3}{4}[/tex] we get;
1 = -k
or
k = -1
⇒equation becomes: b = -a
Therefore, an equation represents this direct variation between a and b is:
[tex]b = -a[/tex] Â Â
The equation that represents this direct variation between a and b is b = -a.
Direct variation is expressed in various mathematical forms.
In equation form, b and vary directly since the ratio of b to a never changes.
The Direct Variation Formula is, b = ka.
Where k is the constant of Variation.
A number b varies directly with the number a.
By definition of direct variation:
b = 2 3/4when a = –2 3/4
Substitute the value of a and b in the formula
[tex]\rm b=ka\\\\2\dfrac{3}{4}=k\times -2\dfrac{3}{4}\\\\-k=1\\\\k=-1[/tex]
Therefore, an equation that represents this direct variation between a and b is b = -a.
Read more about direct variation here;
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