Parallel Lines (Copy)
Q1 (Non-Calculator)
Find the gradient and y-intercept of the line y = 5x – 4.
Solution:
Gradient = 5
Y-intercept = –4
Answer:
Gradient = 5
Y-intercept = –4
Q2 (Non-Calculator)
Find the equation of the line parallel to y = –2x + 1 that passes through (3, 4).
Solution:
Gradient = –2
Equation form: y = –2x + c
Substitute x = 3 and y = 4:
4 = –2(3) + c
4 = –6 + c
c = 4 + 6
c = 10
Equation: y = –2x + 10
Answer: y = –2x + 10
Q3 (Non-Calculator)
Find the equation of the line parallel to y = 0.5x – 6 that passes through (–4, 2).
Solution:
Gradient = 0.5
Equation form: y = 0.5x + c
Substitute x = –4 and y = 2:
2 = 0.5(–4) + c
2 = –2 + c
c = 2 + 2
c = 4
Equation: y = 0.5x + 4
Answer: y = 0.5x + 4
Q4 (Non-Calculator)
The line y = –x + 4 is given. Find the equation of the line parallel to this that passes through (3, 1).
Solution:
Gradient = –1
Equation form: y = –x + c
Substitute x = 3 and y = 1:
1 = –(3) + c
1 = –3 + c
c = 1 + 3
c = 4
Equation: y = –x + 4
Answer: y = –x + 4
Q5 (Non-Calculator)
Find the equation of a line parallel to y = 7x – 9 that passes through (0, –2).
Solution:
Gradient = 7
Equation form: y = 7x + c
Substitute x = 0 and y = –2:
–2 = 7(0) + c
–2 = c
Equation: y = 7x – 2
Answer: y = 7x – 2
Q6 (Calculator)
Find the equation of the line parallel to y = 0.5x – 1 that passes through (4, 3).
Solution:
Gradient = 0.5
Equation form: y = 0.5x + c
Substitute x = 4 and y = 3:
3 = 0.5(4) + c
3 = 2 + c
c = 3 – 2
c = 1
Equation: y = 0.5x + 1
Answer: y = 0.5x + 1
Q7 (Calculator)
Find the equation of the line parallel to y = –2x + 6 that passes through (–3, 5).
Solution:
Gradient = –2
Equation form: y = –2x + c
Substitute x = –3 and y = 5:
5 = –2(–3) + c
5 = 6 + c
c = 5 – 6
c = –1
Equation: y = –2x – 1
Answer: y = –2x – 1
Q8 (Calculator)
Find the equation of the line parallel to y = 4x that passes through (1, –2).
Solution:
Gradient = 4
Equation form: y = 4x + c
Substitute x = 1 and y = –2:
–2 = 4(1) + c
–2 = 4 + c
c = –2 – 4
c = –6
Equation: y = 4x – 6
Answer: y = 4x – 6
Q9 (Calculator)
Find the equation of the line parallel to y = –3x + 7 that passes through (5, –1).
Solution:
Gradient = –3
Equation form: y = –3x + c
Substitute x = 5 and y = –1:
–1 = –3(5) + c
–1 = –15 + c
c = –1 + 15
c = 14
Equation: y = –3x + 14
Answer: y = –3x + 14
Q10 (Calculator)
Find the equation of the line parallel to y = –5x + 4 that passes through (–2, 6).
Solution:
Gradient = –5
Equation form: y = –5x + c
Substitute x = –2 and y = 6:
6 = –5(–2) + c
6 = 10 + c
c = 6 – 10
c = –4
Equation: y = –5x – 4
Answer: y = –5x – 4