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The graph of the line $y = -x + 4$ is shown below - Junior Cycle Mathematics - Question 14 - 2014

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Question 14

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The graph of the line $y = -x + 4$ is shown below. (i) Using the same axes and scales, draw the graph of the line $y = x + 2$. (ii) From the graphs, state the poin... show full transcript

Worked Solution & Example Answer:The graph of the line $y = -x + 4$ is shown below - Junior Cycle Mathematics - Question 14 - 2014

Step 1

Using the same axes and scales, draw the graph of the line y = x + 2.

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Answer

To draw the graph of the line y=x+2y = x + 2:

  1. Identify the y-intercept: The line cuts the y-axis at (0, 2).
  2. Identify another point: If x=−2x = -2, then y=−2+2=0y = -2 + 2 = 0, giving the point (-2, 0).
  3. Plot the points: Mark (0, 2) and (-2, 0) on the graph.
  4. Draw the line: Connect the points with a straight line, ensuring it extends in both directions.

Step 2

From the graphs, state the point of intersection of the two lines.

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Answer

The point of intersection of the two lines can be identified as (1, 3).

Step 3

Verify your answer to (ii) using algebra.

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Answer

To verify the point of intersection (1, 3) using algebra:

  1. Substitute into the equations of both lines:

    • For the first line:

      y=−x+4y = -x + 4
      Substituting x=1x = 1, we get: y=−1+4=3y = -1 + 4 = 3

    • For the second line:

      y=x+2y = x + 2
      Substituting x=1x = 1, we get: y=1+2=3y = 1 + 2 = 3

  2. Result: Since both equations yield y=3y = 3 when x=1x = 1, we can confirm that the point of intersection is indeed (1, 3).

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