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Fill in the three missing entries in the table - Junior Cycle Mathematics - Question 8 - 2011

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Fill in the three missing entries in the table. (a) Line: | Slope | Point where the line crosses the y-axis | Equation ----------------|-------|-------------... show full transcript

Worked Solution & Example Answer:Fill in the three missing entries in the table - Junior Cycle Mathematics - Question 8 - 2011

Step 1

Fill in the missing entries in the table

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Answer

For line k:

  • The slope is calculated from the equation. Given that the y-intercept is (0, -1) and points are aligned with the slope, we derive that:

    • To find it, use the slope formula:

    m=y2−y1x2−x1=−1−40−0=−5−1=2m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 4}{0 - 0} = \frac{-5}{-1} = 2

Thus, the slope for line k is 2.

For line r:

  • The point where it crosses the y-axis needs to be deduced from its equation. Given that it has a slope of -5, the equation having the form:

  • In the standard form, it's represented as:

    y=−5x+8y = -5x + 8

Where the intercept (when x = 0) yields a point crossing at (0, 8) or a corresponding check confirms.

Consequently, fill in these details in the table.

Step 2

Which of these lines is the steepest?

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Answer

Among the lines l, k, r, and t, line r has the steepest slope with a value of -5, while line t has a positive slope equal to 7. Generally, the steepness of a line is determined by the absolute value of its slope:

  • Line l: 3
  • Line k: 2
  • Line r: |-5| = 5
  • Line t: 7

Hence, I would choose line t because it has the largest slope.

Step 3

Is the point (2, 10) on the line l (y = 3x + 4)?

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Answer

To determine whether (2, 10) lies on the line defined by the equation: y=3x+4y = 3x + 4

Substituting x = 2: y=3(2)+4=6+4=10y = 3(2) + 4 = 6 + 4 = 10

Since the result yields y = 10, we can confirm:

  • The point (2, 10) is on line l.

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