An equation for a linear function is shown. \[ y=4 x+12 \] What are the \( x \)-intercept and the \( y \)-intercept of the graph of the function? A. \( \bar{x} \)-intercept \( (-3,0) \) B. \( x \)-intercept \( (0,12) \) \( y \)-intercept: \( (0,12) \) \( y \)-intercept \( (-3,0) \) C. \( x \)-intercept \( (0,12) \) D. \( x \)-intercept \( (4,0) \) \( y \)-intercept \( (4,0) \)

Let's break down the function \( y = 4x + 12 \) to find the intercepts! To find the \( y \)-intercept, we set \( x = 0 \). So, \( y = 4(0) + 12 = 12 \). Thus, the \( y \)-intercept is \( (0, 12) \). Now, for the \( x \)-intercept, we set \( y = 0 \): \[ 0 = 4x + 12 \] Solving this gives \( 4x = -12 \) or \( x = -3 \). Hence, the \( x \)-intercept is \( (-3, 0) \)! The correct answer from the options provided is: \( x \)-intercept \( (-3, 0) \) and \( y \)-intercept \( (0, 12) \). Now, ready for some math fun? Did you know that linear equations trace straight lines on the graph? You could literally draw a line from the \( y \)-intercept to the \( x \)-intercept to illustrate how the function behaves between these points. It visually represents the relationship between \( x \) and \( y \)! Also, don’t shy away from experimenting with other values of \( x \) and \( y \)! Create a table of values and plot a few points. You could find that as \( x \) increases, \( y \) rises sharply because of that steep slope of 4! This way, you can get a better hands-on understanding of the linear relationship. Happy graphing!