Answer :
To create an equation showing Sakeem's profit when laying sod, let's break down the problem:
1. Understand the Direct Variation: The problem states that Sakeem's profit varies directly with the number of square feet of sod he lays. This means that the profit [tex]\( y \)[/tex] is a direct proportion of the square feet of sod [tex]\( x \)[/tex]. The equation for direct variation is usually in the form [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality.
2. Identify the Constant of Proportionality: From the list of numbers provided ([tex]\(1.57\)[/tex], [tex]\(x\)[/tex], [tex]\(y^2\)[/tex], [tex]\(2.00\)[/tex], [tex]\(0.43\)[/tex], [tex]\(y\)[/tex], [tex]\(x^2\)[/tex]), we need to choose the constant that represents [tex]\( k \)[/tex]. According to the information, we use [tex]\( k = 1.57 \)[/tex].
3. Formulate the Equation: Combine the constant of proportionality [tex]\( k \)[/tex] with [tex]\( x \)[/tex] in the direct variation equation:
[tex]\[
y = 1.57x
\][/tex]
4. Conclusion: This equation shows that for every square foot of sod Sakeem lays, his profit [tex]\( y \)[/tex] increases by [tex]\( 1.57 \)[/tex] times the number of square feet laid. Thus, if Sakeem lays [tex]\( x \)[/tex] square feet of sod, his profit will be [tex]\( 1.57 \times x \)[/tex].
This is a clear and accurate representation of the relationship between Sakeem's profit and the area of sod he lays.
1. Understand the Direct Variation: The problem states that Sakeem's profit varies directly with the number of square feet of sod he lays. This means that the profit [tex]\( y \)[/tex] is a direct proportion of the square feet of sod [tex]\( x \)[/tex]. The equation for direct variation is usually in the form [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality.
2. Identify the Constant of Proportionality: From the list of numbers provided ([tex]\(1.57\)[/tex], [tex]\(x\)[/tex], [tex]\(y^2\)[/tex], [tex]\(2.00\)[/tex], [tex]\(0.43\)[/tex], [tex]\(y\)[/tex], [tex]\(x^2\)[/tex]), we need to choose the constant that represents [tex]\( k \)[/tex]. According to the information, we use [tex]\( k = 1.57 \)[/tex].
3. Formulate the Equation: Combine the constant of proportionality [tex]\( k \)[/tex] with [tex]\( x \)[/tex] in the direct variation equation:
[tex]\[
y = 1.57x
\][/tex]
4. Conclusion: This equation shows that for every square foot of sod Sakeem lays, his profit [tex]\( y \)[/tex] increases by [tex]\( 1.57 \)[/tex] times the number of square feet laid. Thus, if Sakeem lays [tex]\( x \)[/tex] square feet of sod, his profit will be [tex]\( 1.57 \times x \)[/tex].
This is a clear and accurate representation of the relationship between Sakeem's profit and the area of sod he lays.
