The table below gives some information about the four lines l, k, r, and t - Junior Cycle Mathematics - Question 8 - 2011
Question 8
The table below gives some information about the four lines l, k, r, and t.
Fill in the three missing entries in the table.
| Line | Slope | Point where the line cr... show full transcript
Worked Solution & Example Answer:The table below gives some information about the four lines l, k, r, and t - Junior Cycle Mathematics - Question 8 - 2011
Step 1
Fill in the missing entries in the table.
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Answer
Line
Slope
Point where the line crosses the y-axis
Equation
l
3
(0, 4)
y = 3x + 4
k
2
(0, -1)
y = 2x - 1
r
-5
(0, 8)
y = -5x + 8
t
7
(0, -6)
y = 7x - 6
Step 2
Which of these lines is the steepest? Tick (✓) one box only.
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Answer
The line t (slope = 7) is the steepest.
Reason: The steepness of a line is determined by its slope; the greater the absolute value of the slope, the steeper the line. Here, line t has the highest slope value.
Step 3
Is the point (2, 10) on the line l (y = 3x + 4)?
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Answer
The point (2, 10) is not on l.
Justification: To check if the point lies on the line, substitute x = 2 into the equation of line l:
y=3(2)+4=6+4=10.
Since the calculated y-value equals the y-coordinate of the point (2, 10), therefore it is confirmed that it indeed lies on the line.
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