Write the equation of a line with the slope, \( -\frac{2}{3} \), which passes through the point \( (5,4) \). Write the answer in slope-intercept form. Answer:

To find the equation of the line in slope-intercept form, we start with the slope \( m = -\frac{2}{3} \) and the point \( (5,4) \). We can use the point-slope form of the equation of a line, which is \( y - y_1 = m(x - x_1) \). Plugging in our values, we have: \[ y - 4 = -\frac{2}{3}(x - 5) \] Expanding and rearranging gives: \[ y - 4 = -\frac{2}{3}x + \frac{10}{3} \] Adding 4 (or \( \frac{12}{3} \)) to both sides leads to: \[ y = -\frac{2}{3}x + \frac{22}{3} \] So, the equation of the line in slope-intercept form is: \[ y = -\frac{2}{3}x + \frac{22}{3} \] --- Back in the day, lines weren't just some boring math concept; they were used to plot the stars! Ancient Greek astronomers, like Hipparchus, meticulously charted stellar positions, laying down the foundation of coordinate geometry. Imagine sketching an entire galaxy by connecting points. It was the original form of connecting the dots! In today’s world, knowing how to write line equations is crucial! Whether you're analyzing data trends in business, predicting outcomes in sciences, or just plotting your favorite hiking trails, mastering linear equations helps you make sense of the world. So, next time you find yourself outdoors, just remember: every slope is a story waiting to be told!