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. - Edexcel - GCSE Maths - Question 14 - 2022 - Paper 2
Question 14
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
The equation of the line L2 is 5y - 10x + 4 = 0
Show that these two lines are parallel. - Edexcel - GCSE Maths - Question 14 - 2022 - Paper 2
Step 1
Convert L2 into slope-intercept form
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Answer
To show that the two lines are parallel, we first need to rewrite the equation of line L2 in slope-intercept form (y = mx + b) where m is the slope. Starting from the equation:
5y - 10x + 4 = 0,
we can isolate y:
5y = 10x - 4
y = 2x - rac{4}{5}.
From this, we can see that the slope of line L2 (m2) is 2.
Step 2
Compare the slopes of L1 and L2
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Answer
Now we need to compare the slopes of both lines. The slope of line L1 (m1) is already given as 2 in the equation y = 2x + 3.
Since both lines have a slope of 2 (m1 = m2 = 2), we conclude that the lines are parallel as they have equal slopes.
