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3. Graph the function and answer each of the following questions. f(x) = 4/3x- 6

a) What is the y-intercept?
b) What is the slope (in fraction form)?
c) Is your slope positive or negative?
d) Explain how you plotted your second point.

1 Answer

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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.

User ABakerSmith
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