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Put a tick (✓) in the correct box to show which point is on the line y = 3x + 8 - Junior Cycle Mathematics - Question 10 - 2017
Question 10
Put a tick (✓) in the correct box to show which point is on the line y = 3x + 8. Justify your answer. The point that is on y = 3x + 8 is: (0, 3) [ ] (8, 0) [ ] (... show full transcript
Worked Solution & Example Answer:Put a tick (✓) in the correct box to show which point is on the line y = 3x + 8 - Junior Cycle Mathematics - Question 10 - 2017
Step 1
Put a tick (✓) in the correct box to show which point is on the line y = 3x + 8.
Answer
To determine which point lies on the line, we will substitute the x-coordinate of each point into the equation and see if the corresponding y-coordinate matches.
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For point (0, 3):
Substitute x = 0 into the equation:
Here, y equals 8, not 3, hence it does not lie on the line.
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For point (8, 0):
Substitute x = 8 into the equation:
Again, y equals 32, not 0, so it does not lie on the line.
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For point (0, 8):
Substitute x = 0 into the equation:
Here, y equals 8 which is a match. Therefore, tick the box for (0, 8).
Step 2
Justification:
Answer
The justification states that the equation of the line is correct and specifies that the computation for the y-value at x = 0 confirms that the point (0, 8) lies on the line. This demonstrates consistency with the mathematical definition of a line in coordinate geometry.
Step 3
Find the point of intersection of the following two lines.
Answer
To find the point of intersection, set the equations equal to one another:
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We have the two equations:
Set them equal:
- Rearranging gives:
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Substitute x = 6 into one of the original equations to find y:
Thus, the point of intersection is (6, 19).