Use what you learned to solve these problems. (6) Jacy's mom teaches cross-stitch classes. The cost of a student's cross-stitch project is a function of the number of skeins of embroidery floss it requires. The table shows the cost of some projects that students can choose. What is the equation of the linear function that models this situation? Show your work.

To find the equation of the linear function that models the situation, we need to determine the slope and the y-intercept of the linear function. Given: - The cost of a student's cross-stitch project is a function of the number of skeins of embroidery floss it requires. - The table shows the cost of some projects that students can choose. From the table, we can see that the cost increases as the number of skeins of embroidery floss increases. This indicates a linear relationship between the cost and the number of skeins. Let's denote the number of skeins of embroidery floss as \( x \) and the cost as \( y \). We can use the two points from the table to find the slope of the linear function. Let's choose the points (2, 10) and (4, 20). The slope of the linear function can be calculated using the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Substitute the values from the points (2, 10) and (4, 20): \[ \text{slope} = \frac{20 - 10}{4 - 2} = \frac{10}{2} = 5 \] Now that we have the slope, we can use one of the points to find the y-intercept. Let's use the point (2, 10). The equation of a linear function in slope-intercept form is given by: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept. Substitute the values of the slope (5) and the point (2, 10) into the equation: \[ 10 = 5(2) + b \] \[ 10 = 10 + b \] \[ b = 0 \] Therefore, the equation of the linear function that models this situation is: \[ y = 5x \] This equation represents the cost of a student's cross-stitch project as a function of the number of skeins of embroidery floss it requires.