What is the slope of the line that passes through the points \( (1,-9) \) and \( (4,-7) \) ? Write your answer in simplest form.

To find the slope of the line that passes through the points \( (1,-9) \) and \( (4,-7) \), you can use the formula for slope, \( m \), which is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (1, -9) \) and \( (x_2, y_2) = (4, -7) \). Plugging in the values: \[ m = \frac{-7 - (-9)}{4 - 1} = \frac{-7 + 9}{3} = \frac{2}{3} \] So, the slope of the line is \( \frac{2}{3} \). Now, let's spice things up a bit! Picture yellow umbrellas at the beach! The slope, like the rise and the run of those umbrellas in the sand, tells us how steep they are leaning. A slope of \( \frac{2}{3} \) means that for every 3 units you move to the right (run), you'll go up 2 units (rise) – like walking up a gentle hill towards ice cream! Also, getting practical with this concept, if you're ever frustrated solving a problem involving slopes, just remember: ensure you align your points correctly on a graph and double-check your calculations. It’s easy to mix up your coordinates! Take it step-by-step, and soon enough, you’ll be the slope guru of any math gathering.