Review Later Identify the slope of a line that passes through point (4, 1) and has a y intercept of 4

To find the slope of the line, you can use the slope-intercept form of a line, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Here, the y-intercept is 4, so \(b = 4\). The line passes through the point (4, 1), meaning when \(x = 4\), \(y = 1\). Plugging these values into the equation gives us: \[ 1 = m(4) + 4 \] Solving for \(m\) yields: \[ 1 = 4m + 4 \] \[ 4m = 1 - 4 \] \[ 4m = -3 \] \[ m = -\frac{3}{4} \] So, the slope of the line is \(-\frac{3}{4}\). Did you know that the concept of slope dates back to ancient civilizations, but it was the Greeks who formalized the ideas? Euclid and his contemporaries laid the groundwork for geometry, including the study of lines and angles. This paved the way for further development in mathematics, influencing generations of mathematicians! Understanding slope isn't just a classroom concept; it has real-world implications, too! For instance, engineers use slope to design roads and buildings. A proper slope ensures vehicles can easily navigate hills and that structures can drain water efficiently—making sure our daily commutes and homes are safe and functional!