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The line h has a slope of 4 and passes through the point (20, 12) - Junior Cycle Mathematics - Question 11 - 2022

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Question 11

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The line h has a slope of 4 and passes through the point (20, 12). Find the co-ordinates of another point on the line h, other than the point (20, 12). Show your wo... show full transcript

Worked Solution & Example Answer:The line h has a slope of 4 and passes through the point (20, 12) - Junior Cycle Mathematics - Question 11 - 2022

Step 1

Find the Equation of the Line

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Answer

The formula for the slope (m) is given by:

m=riserunm = \frac{rise}{run}

Given that the slope is 4 and using the point (20, 12), we can write the equation of the line in point-slope form:

y−y1=m(x−x1)y - y_1 = m(x - x_1)

Substituting the values, we get:

y−12=4(x−20)y - 12 = 4(x - 20)

Now expand and simplify the equation:

y−12=4x−80y - 12 = 4x - 80

Thus,

y=4x−68y = 4x - 68

Step 2

Find Another Point on the Line

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Answer

Now that we have the equation of the line, we can choose any value for x to find another point.

Let's choose x = 21:

y=4(21)−68y = 4(21) - 68

Calculating this:

y=84−68y = 84 - 68 y=16y = 16

Therefore, another point on the line h, other than (20, 12), is (21, 16).

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