\[ y-7=-\frac{1}{3}(x+9) \] (Simplify your answer. Use integers or fractions for any numbers in the equation.) What is the slope-intercept form of the equation of the line? \( \square \) (Simplify your answer. Use integers or fractions for any numbers in the equation.) W

To convert the equation \( y-7=-\frac{1}{3}(x+9) \) into slope-intercept form, start by distributing the \(-\frac{1}{3}\): \[ y - 7 = -\frac{1}{3}x - 3 \] Next, add 7 to both sides: \[ y = -\frac{1}{3}x - 3 + 7 \] This simplifies to: \[ y = -\frac{1}{3}x + 4 \] So, the slope-intercept form of the equation is \( y = -\frac{1}{3}x + 4 \). Every line has a story, and the slope-intercept form is one of the best ways to tell it! It not only captures the steepness of the line (the slope) but also its starting position on the y-axis (the y-intercept). This form is super handy for quickly graphing lines or comparing slopes when determining if lines are parallel, intersecting, or perpendicular. In the real world, understanding the slope-intercept form is critical in various fields, such as economics, where it can model cost functions, or in physics, where it might represent speed and time. By breaking down the relationship between variables in this straightforward way, you can make predictions and informed decisions based on those models.