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The line h has a slope of -2 - Junior Cycle Mathematics - Question 8 - 2018

Question 8

The line h has a slope of -2. It passes through the point (1, 101). Find how many points on this line have co-ordinates that are both positive whole numbers, includ... show full transcript

Worked Solution & Example Answer:The line h has a slope of -2 - Junior Cycle Mathematics - Question 8 - 2018

Step 1

Determine the slope and equation of the line

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Answer

Given that the slope (m) is -2 and the line passes through (1, 101), we can use the point-slope form of the equation of the line:

$y - y_1 = m(x - x_1)$

Substituting the values gives us:

$y - 101 = -2(x - 1)$

Rearranging it, we find:

$y = -2x + 103$

Step 2

Identify conditions for positive whole number coordinates

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Answer

For coordinates (x, y) to be positive whole numbers, both x and y must be greater than 0. Since the equation is linear, we need to find the x-values where y remains positive.

Setting y > 0:

$-2x + 103 > 0$

Solving for x gives:

$2x < 103$

$x < 51.5$

The possible integer values for x range from 1 to 51 (since x must be a whole number).

Step 3

Calculate the number of valid points

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Answer

The integer values of x run from 1 to 51, inclusive. That gives us:

$51 - 1 + 1 = 51$

Thus, there are 51 points where both coordinates are positive whole numbers.

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