Sure! Let's solve this step-by-step.
### Step a) Find the equation that relates [tex]\( y \)[/tex] and [tex]\( x \)[/tex].
Since [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], it can be expressed in the form:
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is the constant of variation. To find [tex]\( k \)[/tex], we use the given values [tex]\( y = 35 \)[/tex] when [tex]\( x = 14 \)[/tex]:
[tex]\[ 35 = k \cdot 14 \][/tex]
Now, solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{35}{14} \][/tex]
[tex]\[ k = 2.5 \][/tex]
So, the equation that relates [tex]\( y \)[/tex] and [tex]\( x \)[/tex] is:
[tex]\[ y = 2.5x \][/tex]
### Step b) What is [tex]\( y \)[/tex] when [tex]\( x = 29 \)[/tex]?
Using the equation [tex]\( y = 2.5x \)[/tex]:
[tex]\[ y = 2.5 \cdot 29 \][/tex]
[tex]\[ y = 72.5 \][/tex]
Therefore, when [tex]\( x = 29 \)[/tex], [tex]\( y \)[/tex] is:
[tex]\[ y = 72.5 \][/tex]
