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Plot points on a Cartesian plan using the table results and join the point.

Mathematics

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Graph of y = x + 2

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Key points of y = x + 2
Pointxy
x-intercept−20
y-intercept02

Step-by-step solution

3 steps

let's complete this table and describe the plot.

6.2.1 Copy and Complete the table

  1. Analyze the given points to find the pattern.

    We have the points (0,2)(0, 2), (2,4)(2, 4), and (4,6)(4, 6).
    Let's find the change in yy (Δy\Delta y) and the change in xx (Δx\Delta x).
    From (0,2)(0, 2) to (2,4)(2, 4): Δx=2−0=2\Delta x = 2-0 = 2, Δy=4−2=2\Delta y = 4-2 = 2.
    From (2,4)(2, 4) to (4,6)(4, 6): Δx=4−2=2\Delta x = 4-2 = 2, Δy=6−4=2\Delta y = 6-4 = 2.
    Since the change in yy is constant for a constant change in xx, this is a linear relationship.

  2. Determine the equation of the line.

    The slope m=ΔyΔx=22=1m = \frac{\Delta y}{\Delta x} = \frac{2}{2} = 1.
    The yy-intercept (cc) is the value of yy when x=0x=0, which is 2.
    So, the equation is y=mx+c  ⟹  y=1x+2  ⟹  y=x+2y = mx + c \implies y = 1x + 2 \implies y = x + 2.

  3. Use the equation to complete the table.

    For x=1x=1: y=1+2=3y = 1 + 2 = 3.
    For x=3x=3: y=3+2=5y = 3 + 2 = 5.

    The completed table is:

    xy0213243546\begin{array}{|c|c|} \hline x & y \\ \hline 0 & 2 \\ \hline 1 & 3 \\ \hline 2 & 4 \\ \hline 3 & 5 \\ \hline 4 & 6 \\ \hline \end{array}

    The final answer for the completed table is:
    xy0213243546\boxed{ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & 2 \\ \hline 1 & 3 \\ \hline 2 & 4 \\ \hline 3 & 5 \\ \hline 4 & 6 \\ \hline \end{array} }

    6.2.2 Plot points on a Cartesian plan using the table results and join the point.

    To plot the points, you would mark the following coordinates on a Cartesian plane:

    • (0,2)(0, 2)
    • (1,3)(1, 3)
    • (2,4)(2, 4)
    • (3,5)(3, 5)
    • (4,6)(4, 6)

    After plotting these points, you would draw a straight line connecting them. This line represents the graph of the equation y=x+2y = x + 2.

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