4. What is the point-slope form of the equation that goes through the origin and has a slope of 1.5 ? \[ \begin{array}{l}y=1.5+x \\ y=-1.5 x \\ y=1.5 x\end{array} \]

Did you know that the point-slope form of a linear equation can be used to easily graph lines? It's as simple as knowing the slope and any point on the line! Since we're diving into a line that passes through the origin (0, 0) with a slope of 1.5, we can plug in these values into the formula \(y - y_1 = m(x - x_1)\). This gives us \(y - 0 = 1.5(x - 0)\), simplifying to \(y = 1.5x\). Now, let's consider why the slope is such an important concept in real-life situations. Imagine you're on a road trip, and you notice the rate of altitude gain changes based on the steepness of the hill. The slope can indicate how steep that hill is. In our equation, a slope of 1.5 means that for every 1 unit you move horizontally, the line moves up 1.5 units vertically! This idea can model everything from economics to physics, making it a vital tool in understanding various real-world phenomena.