The graph of the line $y = x + 1$ is shown on the co-ordinate grid below. (a) Write down the co-ordinates of the point where this line crosses the $y$-axis. (b) Write down the co-ordinates of the point where the line $y = x + 4$ crosses the $y$-axis. Answer: (c) Hence, or otherwise, draw the graph of the line $y = x + 4$ on the co-ordinate grid above.

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The graph of the line $y = x + 1$ is shown on the co-ordinate grid below - Junior Cycle Mathematics - Question 12 - 2015

Question 12

The graph of the line $y = x + 1$ is shown on the co-ordinate grid below. (a) Write down the co-ordinates of the point where this line crosses the $y$-axis. (b) Wr... show full transcript

Worked Solution & Example Answer:The graph of the line $y = x + 1$ is shown on the co-ordinate grid below - Junior Cycle Mathematics - Question 12 - 2015

Step 1

Write down the co-ordinates of the point where this line crosses the y-axis.

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Answer

The line $y = x + 1$ crosses the $y$ -axis when $x = 0$ . Substituting $x = 0$ in the equation yields:

$y = 0 + 1 = 1.$

Thus, the coordinates are $(0, 1)$ .

Step 2

Write down the co-ordinates of the point where the line y = x + 4 crosses the y-axis.

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Answer

The line $y = x + 4$ crosses the $y$ -axis when $x = 0$ . Substituting $x = 0$ in the equation gives:

$y = 0 + 4 = 4.$

Therefore, the coordinates are $(0, 4)$ .

Step 3

Hence, or otherwise, draw the graph of the line y = x + 4 on the co-ordinate grid above.

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Answer

To draw the line $y = x + 4$ , we can identify two key points:

When $x = 0$ , $y = 4$ gives the point $(0, 4)$ .
When $x = 1$ , $y = 5$ gives the point $(1, 5)$ .

Plot these points on the graph and draw a straight line through them to represent the equation $y = x + 4$ .

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