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Given points P(2, 9), Q(6, 3), R(2, -3), and S(-4, 3), and the equation y = 1/2x + 3, plot the points and graph the equation.

Mathematics

ScanSolve AI Answer

Graph of y = 1/2x + 3

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Key points of y = 1/2x + 3
Pointxy
x-intercept−60
y-intercept03

Step-by-step solution

3 steps
  1. Write the coordinates for points P, Q, R, and S from the graph.

    • Point P is at (2,9)(2, 9).
    • Point Q is at (6,3)(6, 3).
    • Point R is at (2,−3)(2, -3).
    • Point S is at (−4,3)(-4, 3).

    The coordinates are:
    P: (2,9)\boxed{(2, 9)}
    Q: (6,3)\boxed{(6, 3)}
    R: (2,−3)\boxed{(2, -3)}
    S: (−4,3)\boxed{(-4, 3)}

  2. Complete the table for the equation y=12x+3y = \frac{1}{2}x + 3.

    • For x=−4x = -4: y=12(−4)+3=−2+3=1y = \frac{1}{2}(-4) + 3 = -2 + 3 = 1
    • For x=−2x = -2: y=12(−2)+3=−1+3=2y = \frac{1}{2}(-2) + 3 = -1 + 3 = 2
    • For x=0x = 0: y=12(0)+3=0+3=3y = \frac{1}{2}(0) + 3 = 0 + 3 = 3
    • For x=2x = 2: y=12(2)+3=1+3=4y = \frac{1}{2}(2) + 3 = 1 + 3 = 4
    • For x=4x = 4: y=12(4)+3=2+3=5y = \frac{1}{2}(4) + 3 = 2 + 3 = 5

    The completed table is:

    x-4-2024
    y12345
  3. Draw the graph of y=12x+3y = \frac{1}{2}x + 3 on the provided grid.

    Plot the points from the table: (−4,1)(-4, 1), (−2,2)(-2, 2), (0,3)(0, 3), (2,4)(2, 4), and (4,5)(4, 5).
    Draw a straight line connecting these points. The graph drawn on the provided grid correctly represents these points and the line.

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