Answer:
Value of b = [tex]\frac{5}{4}[/tex] =1.25.
Step-by-step explanation:
Direct Variation states that a relationship between two variables in which one is a constant multiple of the other.
*if one variable changes the other changes in proportion to the first.
*If a is directly proportional to b i.e,
[tex]a \propto b[/tex] then it is of the form
a = kb ;where k is constant variation.
Given: a varies directly as b;
then, by definition of direct variation;
we have;
[tex]a = kb[/tex] .....[1]
Substitute the value of a =28 and b =7 to solve for k;
[tex]28 = k(7)[/tex]
Divide both sides by 7 we have;
[tex]\frac{28}{7}=\frac{7k}{7}[/tex]
Simplify:
k =4
now, find b using same method when a =5;
then;
after substituting the value of a = 5 and k=4 in [1] ;
[tex]5=(4)b[/tex]
Divide by 4 to both sides we get;
[tex]b =\frac{5}{4}[/tex]
Therefore, the value of b = [tex]\frac{5}{4}[/tex] =1.25
