The equation of the line L1 is $y = 2x + 3$ - Edexcel - GCSE Maths - Question 13 - 2022 - Paper 2
Question 13
The equation of the line L1 is $y = 2x + 3$.
The equation of the line L2 is $5y - 10x + 4 = 0$.
Show that these two lines are parallel.
Worked Solution & Example Answer:The equation of the line L1 is $y = 2x + 3$ - Edexcel - GCSE Maths - Question 13 - 2022 - Paper 2
Rewrite the equation of line L2
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Start by rearranging the equation of line L2 to the slope-intercept form (y = mx + b).
Given:
5y−10x+4=0
Add 10x to both sides:
5y=10x−4
Now, divide every term by 5:
y = 2x - rac{4}{5}
Identify the slopes of the lines
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From the equation of line L1, which is y=2x+3, we can see that the slope (m) is 2.
From the rearranged equation of line L2, y = 2x - rac{4}{5}, the slope is also 2.
Thus, both lines have the same slope, which is an essential characteristic of parallel lines.
Conclusion
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Since both line L1 and line L2 have the same slope of 2, we can conclude that these two lines are parallel.
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