Construct a linear function that has a slope of -3 and passes through the point \( (-2,3) \)

To construct a linear function with a slope of -3 that passes through the point \((-2,3)\), we can use the point-slope form of a linear equation: \[ y - y_1 = m(x - x_1) \] Here, \(m\) is the slope, and \((x_1, y_1)\) is the point. Substituting the given values: \[ y - 3 = -3(x + 2) \] Now, simplifying this: \[ y - 3 = -3x - 6 \] \[ y = -3x - 3 \] And there you have the linear function: \[ y = -3x - 3 \] This function tells you that for every unit increase in \(x\), \(y\) decreases by 3 units. The beauty of linear functions is in their simplicity! They represent straight lines in a graph where every point along the line is a solution to the equation. Imagine plotting this function: the line would slant downwards steeply because of the negative slope. You could use this to model real-world scenarios, like predicting costs that decrease over time or measuring loss of value in an asset.