Final answer:
The y-intercept of the linear function f(x) = 4/3x - 6 is -6, the slope is 4/3 which is positive, and the graph's second point is plotted by rising 4 units up and running 3 units right from the y-intercept.
Step-by-step explanation:
The linear function given is f(x) = \(\frac{4}{3}\)x - 6. To graph this function and find the requested information, use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
- The y-intercept is the point where the graph crosses the y-axis (x=0). For the function f(x) = \(\frac{4}{3}\)x - 6, it is -6. This can be seen from the equation because it is the constant term.
- The slope is \(\frac{4}{3}\), taken directly from the coefficient of the x term in the equation. Therefore, the slope in fraction form is \(\frac{4}{3}\).
- The slope is positive, as indicated by the positive coefficient of the x term.
- To plot the second point, start at the y-intercept (0, -6) and use the slope to rise up 4 units and run to the right 3 units. Place a point at the new location (3, -2). Connect these two points with a straight line to complete the graph.