A line has a slope of \( -\frac{7}{3} \) and a \( y \)-intercept of -4 . Write its equation in slope-intercept form Write your answer using integers, proper fractions, and improper fractions in simplest fort

To write the equation of the line in slope-intercept form, we use the formula \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. Given the slope \( m = -\frac{7}{3} \) and the \( y \)-intercept \( b = -4 \), we can plug these values into the formula: \[ y = -\frac{7}{3}x - 4 \] To express -4 as a fraction, we rewrite it as \( -\frac{12}{3} \), allowing us to combine terms later if needed. Thus, the equation can also be represented in a slightly different format: \[ y = -\frac{7}{3}x - \frac{12}{3} \] This highlights the slope-intercept form clearly! --- Did you know that the slope-intercept form of a line makes visualizing graphs a breeze? With just the slope and \( y \)-intercept, you can sketch the line quickly: start at the \( y \)-intercept on the graph, and then use the slope to find another point by moving down 7 units (because of the negative slope) and right 3 units! Understanding slope can also help when you deal with real-world situations, like optimizing routes in navigation or determining how steep a hill is for constructing roads. Using slopes can simplify complex problems in various practical scenarios, whether in architecture, transportation, or even sports statistics!