Find the equation (in terms of x) of the line through the points (-2,4) and (4,-14). y=

To find the equation of the line in terms of \( y \) and \( x \), we'll first calculate the slope \( m \) using the two points \( (-2, 4) \) and \( (4, -14) \). The formula for the slope is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-14 - 4}{4 - (-2)} = \frac{-18}{6} = -3. \] Next, we can use the point-slope form of a line equation, \( y - y_1 = m(x - x_1) \). Taking point \( (-2, 4) \): \[ y - 4 = -3(x + 2). \] Expanding this gives: \[ y - 4 = -3x - 6. \] Adding 4 to both sides, we find: \[ y = -3x - 2. \] So the equation of the line in terms of \( x \) is: \[ y = -3x - 2. \] Now, as a fun fact, did you know that the slope of a line represents its steepness? A negative slope, like ours (-3), indicates that as \( x \) increases, \( y \) decreases—like going down a slide! Additionally, in real-world applications, lines can represent trends, such as the relationship between time and distance traveled. For example, if you plot the distance a car travels over time, the slope can show how fast it's going. A steeper line indicates greater speed!