A line passes through the point \( (-5,4) \) and has a slope of -2 . Write an equation in slope-intercept form for this line.

To write the equation of a line in slope-intercept form (y = mx + b), we start with the slope (m) and a point on the line. Here, our slope is -2 and the point is (-5, 4). Using the point-slope form: \[ y - y_1 = m(x - x_1) \] Substituting in our values: \[ y - 4 = -2(x + 5) \] Distributing the -2 gives: \[ y - 4 = -2x - 10 \] Adding 4 to both sides: \[ y = -2x - 6 \] So, the equation of the line in slope-intercept form is \( y = -2x - 6 \). To make the math feel a bit more playful, consider this: Every straight line has its own unique dance move! This slope of -2 means it descends quickly—one step to the right, and it goes two steps down! Now let’s have a little fun with real-world applications. Imagine you're tracking how the temperature changes during the evening. If you know that the temperature at a certain point is 4 degrees but drops by 2 degrees every hour, you could use a similar equation to predict how cold it’ll get at different times! This mathematical relationship isn’t just for lines; it's a great way to understand all sorts of trends!