Answer :
To solve this problem, we need to create an equation to represent Sakeem's profit when laying sod. Let's break it down step-by-step:
1. Identify the Variables:
- [tex]\( y \)[/tex] represents Sakeem's profit.
- [tex]\( x \)[/tex] represents the number of square feet of sod he lays.
2. Understand Direct Variation:
Since the profit varies directly with the number of square feet of sod, we can express this relationship as:
[tex]\[
y = k \times x
\][/tex]
where [tex]\( k \)[/tex] is a constant representing the rate of profit per square foot.
3. Use the Given Labels to Form the Equation:
- From the given choices, we must identify which constant multiplies with [tex]\( x \)[/tex] to result in the profit [tex]\( y \)[/tex].
- Considering the context and the relation defined, the hint given is [tex]\( 0.43 \)[/tex] which fits as the multiplier of [tex]\( x \)[/tex].
4. Formulate the Equation:
[tex]\[
y = 0.43 \times x
\][/tex]
This equation signifies that for each square foot of sod laid, Sakeem makes a profit of [tex]\( 0.43 \)[/tex], which is the direct relationship or constant rate of profit.
Therefore, the direct variation equation for Sakeem's profit when laying sod is:
[tex]\[
y = 0.43 \times x
\][/tex]
This means that as the number of square feet [tex]\( x \)[/tex] increases, the profit [tex]\( y \)[/tex] increases proportionally by the constant multiplier [tex]\( 0.43 \)[/tex].
1. Identify the Variables:
- [tex]\( y \)[/tex] represents Sakeem's profit.
- [tex]\( x \)[/tex] represents the number of square feet of sod he lays.
2. Understand Direct Variation:
Since the profit varies directly with the number of square feet of sod, we can express this relationship as:
[tex]\[
y = k \times x
\][/tex]
where [tex]\( k \)[/tex] is a constant representing the rate of profit per square foot.
3. Use the Given Labels to Form the Equation:
- From the given choices, we must identify which constant multiplies with [tex]\( x \)[/tex] to result in the profit [tex]\( y \)[/tex].
- Considering the context and the relation defined, the hint given is [tex]\( 0.43 \)[/tex] which fits as the multiplier of [tex]\( x \)[/tex].
4. Formulate the Equation:
[tex]\[
y = 0.43 \times x
\][/tex]
This equation signifies that for each square foot of sod laid, Sakeem makes a profit of [tex]\( 0.43 \)[/tex], which is the direct relationship or constant rate of profit.
Therefore, the direct variation equation for Sakeem's profit when laying sod is:
[tex]\[
y = 0.43 \times x
\][/tex]
This means that as the number of square feet [tex]\( x \)[/tex] increases, the profit [tex]\( y \)[/tex] increases proportionally by the constant multiplier [tex]\( 0.43 \)[/tex].
