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Complete Table 2 on the relation y = -2x + 3, for the values of x from -3 to +5. (b) Use a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, draw the graph of the equation y = -2x + 3. (c) From the graph, determine the value of: (i) the slope; (ii) x when y = -5.

Mathematics

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2 parts

Step-by-step solution

5 steps

Part a· 2 steps

To complete Table 2, substitute each value of xx into the relation y=−2x+3y = -2x + 3.

  1. Calculate yy for each xx value.

    For x=−2x = -2: y=−2(−2)+3=4+3=7y = -2(-2) + 3 = 4 + 3 = 7
    For x=−1x = -1: y=−2(−1)+3=2+3=5y = -2(-1) + 3 = 2 + 3 = 5
    For x=0x = 0: y=−2(0)+3=0+3=3y = -2(0) + 3 = 0 + 3 = 3
    For x=2x = 2: y=−2(2)+3=−4+3=−1y = -2(2) + 3 = -4 + 3 = -1
    For x=3x = 3: y=−2(3)+3=−6+3=−3y = -2(3) + 3 = -6 + 3 = -3
    For x=4x = 4: y=−2(4)+3=−8+3=−5y = -2(4) + 3 = -8 + 3 = -5

  2. Complete the table with the calculated values.

    x−3−2−1012345y97531−1−3−5−7\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline y & 9 & 7 & 5 & 3 & 1 & -1 & -3 & -5 & -7 \\ \hline \end{array}

Part b

To draw the graph of the equation y=−2x+3y = -2x + 3, plot the points from the completed table: (−3,9),(−2,7),(−1,5),(0,3),(1,1),(2,−1),(3,−3),(4,−5),(5,−7)(-3, 9), (-2, 7), (-1, 5), (0, 3), (1, 1), (2, -1), (3, -3), (4, -5), (5, -7).

Use the given scale: 2 cm2 \text{ cm} to 1 unit1 \text{ unit} on the xx-axis and 2 cm2 \text{ cm} to 2 units2 \text{ units} on the yy-axis. Connect the points with a straight line.
(As an AI, I cannot draw the graph for you, but these are the points you would plot.)

Part c(i)-2

the slope;

From the graph, determine the value of

The equation is y=−2x+3y = -2x + 3, which is in the form y=mx+cy = mx + c, where mm is the slope.

  1. Identify the slope from the equation.

    The coefficient of xx is the slope.
    The slope is −2\boxed{-2}.

Part c(ii)4

xx when y=−5y = -5.

  1. Substitute y=−5y = -5 into the equation y=−2x+3y = -2x + 3.

    −5=−2x+3-5 = -2x + 3
  2. Solve for xx.

    −5−3=−2x-5 - 3 = -2x −8=−2x-8 = -2x x=−8−2x = \frac{-8}{-2} x=4x = \boxed{4}
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