Carolina está cortando gramados como trabalho de verão. Para cada trabalho que ela consegue, ela cobra úma taxa inicial mais 6 por hora de trabalho. Sua taxa total para um trabalho de 4horas, por exemplo, é de 32 Considere ya taxa de Carolina (em reais) por um único trabalho que levou zhoras para ser concluído. Complete a equação da relação entre a taxa e o número de horas. y=

## Step 1: Identify the relationship<br />### The problem describes a linear relationship between the total fee Carolina charges (\(y\)) and the number of hours she works (\(x\)). This relationship can be represented by a linear equation in the form \(y = mx + b\), where \(m\) is the slope (or the rate of change) and \(b\) is the y-intercept (or the initial fee).<br />## Step 2: Determine the slope<br />### From the problem, we know that Carolina charges \$6 per hour of work. This is our rate of change, or the slope \(m\).<br />## Step 3: Calculate the y-intercept<br />### We also know that for a 4-hour job, Carolina charges \$32. We can use this information to find the initial fee, or the y-intercept \(b\). We substitute \(y = 32\), \(m = 6\), and \(x = 4\) into the equation \(y = mx + b\) and solve for \(b\):<br />\[<br />32 = 6 \cdot 4 + b<br />\]<br />\[<br />32 = 24 + b<br />\]<br />\[<br />b = 32 - 24<br />\]<br />\[<br />b = 8<br />\]<br />## Step 4: Formulate the equation<br />### Therefore, the equation that represents the relationship between the total fee \(y\) and the number of hours \(x\) is:<br />\[<br />y = 6x + 8<br />\]