A line has a slope of \( \frac{5}{3} \) and a \( y \)-intercept of \( -\frac{2}{3} \), 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 \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. For the line with a slope of \( \frac{5}{3} \) and a \( y \)-intercept of \( -\frac{2}{3} \), the equation would be: \[ y = \frac{5}{3}x - \frac{2}{3} \] Now, to make it more visually appealing, we can multiply through by 3 to eliminate the fractions, resulting in: \[ 3y = 5x - 2 \] So, the equation is \( y = \frac{5}{3}x - \frac{2}{3} \) or \( 3y = 5x - 2 \) in integer form! Visualizing slope and intercept helps; imagine a bustling city street where slopes represent incline or decline. The higher the slope, the steeper the hill! A \( \frac{5}{3} \) slope means for every 3 units you move right, you move up 5 units. Now think of the \( y \)-intercept as where you’d plant your roots—at \( -\frac{2}{3} \), you’re a hair below the origin, ready to head uphill! Looking for more about lines? Dive into the interesting world of linear functions and their applications! Discover how they define relationships like speed and distance or even economics—like the best price for potato chips. Books or online articles on graphing functions can really expand your insight into math and its real-life magic!