Job A will give you \( \$ 100 \) to start with them and pay you \( \$ 50 \) a day. Job B will give you \( \$ 800 \) to start with and pay you \( \$ 40 \) a day. Write an equation for each, then graph. Label your graph!! When is Job \( A \) the best deal? Write your answer in interval notation!!

Let's denote \( x \) as the number of days worked. For Job A, the total earnings can be represented by the equation: \[ E_A = 100 + 50x \] For Job B, the total earnings equation is: \[ E_B = 800 + 40x \] To find when Job A is the better deal, we need to set the two equations equal: \[ 100 + 50x < 800 + 40x \] Now, let's solve for \( x \): 1. Subtract \( 40x \) from both sides: \[ 100 + 10x < 800 \] 2. Subtract \( 100 \) from both sides: \[ 10x < 700 \] 3. Divide by \( 10 \): \[ x < 70 \] Now, let's summarize: Job A is the better option for \( x \) in the interval notation \( (-\infty, 70) \). ### Graphing: To graph these equations, plot two lines on a coordinate system where the x-axis represents days and the y-axis represents total earnings. **For Job A (green line)**: Start at \( (0, 100) \) and go up by \( 50 \) every day (slope of 50). **For Job B (blue line)**: Start at \( (0, 800) \) and go up by \( 40 \) every day (slope of 40). Label your graph accordingly, and shade the region below the line from Job A where it is the best deal until day \( 70 \).