What is the equation of the line that passes through the points \( (0,4) \) and \( (9,-5) ? \) \( \begin{array}{llll}\text { a) } y=x+4 & \text { b) } y=-x+4 & \text { c) } y=-1 x-3 & \text { d) } y=1 x+5\end{array} \) Oa Ob Oc Od

To find the equation of the line passing through the points \( (0,4) \) and \( (9,-5) \), we first calculate the slope \( m \) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 4}{9 - 0} = \frac{-9}{9} = -1 \] Now, we use the slope-intercept form of the equation \( y = mx + b \). The y-intercept \( b \) can be obtained from the point \( (0,4) \) where \( y = 4 \). Thus, we have: \[ y = -1x + 4 \] So the equation simplifies to \( y = -x + 4 \), which corresponds to option (b). Now, if you're intrigued by how such equations have evolved over time, line equations have been used since the time of Euclid in ancient Greece, serving as a fundamental concept in geometry. And if you ever find yourself grappling with lines in programming, remember that many coding languages allow you to manipulate lines and calculate intersections with straightforward functions that can help you visualize and solve complex problems!