A line has a slope of -4 and a \( y \)-intercept of 0 . Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

The equation of a line in slope-intercept form is given by the formula \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. Given that the slope is -4 and the \( y \)-intercept is 0, we can substitute these values into the formula: \[ y = -4x + 0 \] This simplifies to: \[ y = -4x \] So, the equation of the line is \( y = -4x \). Now, let's take a moment to appreciate that this means for every unit you move to the right (positive \( x \)), the line falls 4 units down. It’s like a steep hill that’s fun to roll down, but certainly a challenge to climb back up! Additionally, real-world applications of the slope can be seen in fields like economics, where negative slopes often represent inversely proportional relationships, such as the increase of prices leading to a decrease in demand. So, on this mathematical ride, you can see how steep slopes and intercepts play a crucial role in understanding trends and making predictions!