1.
A straight line has equation y = 4x – 5. (a)
Find the value of x when y = 1.
x = …………………………. (2)
(b)
Write down the equation of the straight line that is parallel to y = 4x – 5 and passes through the point (0, 3).
……………………………… (2)
(c)
Rearrange the equation y = 4x – 5 to find x in terms of y.
x = …………………………. (2) (Total 6 marks)
2.
A straight line, L, passes through the point with coordinates (4, 7) and is perpendicular to the line with equation y = 2x + 3. Find an equation of the straight line L.
……………………………… (Total 3 marks)
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3.
The diagram shows three points A (–1, 5), B (2, – 1) and C (0, 5). A line L is parallel to AB and passes through C. Find the equation of the line L.
……………………. (Total 4 marks)
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4.
A straight line has equation y = 2x – 3 The point P lies on the straight line. The y coordinate of P is –4 (a)
Find the x coordinate of P.
................................. (2)
A straight line L is parallel to y = 2x – 3 and passes through the point (3,4). (b)
Find the equation of line L.
................................. (3) (Total 5 marks)
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5.
A straight line has equation y = 2x – 3 The point P lies on the straight line. The y coordinate of P is –4 (a)
Find the x coordinate of P.
................................... (2)
A straight line L is parallel to y = 2x – 3 and passes through the point (3,4). (b)
Find the equation of line L.
...................................... (3)
y = 12 x − 3 y = 3 − 12 x y = 2x – 3
(c)
y=3– 2 x
y = 2x + 3
Put a tick ( ) underneath the equation which is the equation of a straight line that is perpendicular to the line with equation y = 2x – 3 (1) (Total 6 marks)
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6.
A straight line, L, has equation 3y = 5x − 6 Find (i)
the gradient of L,
……………… (ii)
the y-co-ordinate of the point where L cuts the y-axis.
(0, ……) (Total 2 marks)
7.
Find the gradient of the straight line with equation 5y = 3 – 2x.
……………………… (Total 2 marks)
8.
A straight line has equation
1 y= 2x+1
The point P lies on the straight line. P has a y-coordinate of 5. (a)
Find the x-coordinate of P.
............................ (2)
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(b)
1 Rearrange y = 2 x + 1 to make x the subject.
..................................... (2) (Total 4 marks)
9.
A straight line has equation (a)
2y − 6x = 5
Find the gradient of the line.
……………………….. (2)
The point (k, 6) lies on the line. (b)
Find the value of k.
k = …………….. (2) (Total 4 marks)
10.
A straight line has equation (a)
y = 5 – 3x
Write down the gradient of the line. ……………………….. (1)
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(b)
Write down the coordinates of the point where the line crosses the y axis.
(…… , ……) (1) (Total 2 marks)
11. P
y
Q
O R
x
S
The diagram shows 4 straight lines, labelled P, Q, R and S. The equations of the straight lines are A: B: C: D:
y = 2x y = 3 − 2x y = 2x + 3 y=3
Match each straight line, P, Q, R and S to its equation. Complete the table. Equation
A
B
C
D
Straight line (Total 2 marks)
12.
(a)
1.5
2
1+ 5 4 1= 4x − 5; 4x = 1 + 5; M1 for attempt to isolate x and divide by 4 A1 for 1.5 oe x=
(b)
y = 4x + 3
2 B2 for y = 4x + 3 (B1 for y = 4x + k, k ≠ − 5)
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(c)
x=
y+5 4
2
4x = y + 5 M1 for correct isolation of x-term y+5 A1 for 4 [6]
13.
1 y = −2 x+9
3
1 − 2 or 2 m = −1 oe 1 y = −2 x+c
B1 for
− 12 or 2m = −1 oe
1 y = −2x+c ,c≠0 1 y = −2 x+9 A1 for oe 0
M1 for
(SC: if 3 then B1 for either y = 2x − 1 oe or y = − 2x + 15 oe) [3]
14.
y = – 2x + 5
4
5 − −1 −1− 2 = – 2 M1 for clear attempt to find gradient eg fraction with – 1, 5 in numerator, 2, – 1 in denominator A1 for – 2 cao
−6 B2 ft for y = “–2”x + 5oe (eg y = 3 x + 5) (B1 for y = mx + 5 or , – 2x + 5 or y = “–2”x + c) [4]
15.
(a)
–4 = 2a – 3 1 – = 2
2
1 M1 for –4 = 2a – 3 or x shown as 2 1 1 – – ,–4 A1 2 or ( 2 )
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(b)
y = 2x + c 4 = 2 × 3 + c, c = –2 y = 2x – 2 M1 for y = 2x + c (c ≠ –3) or gradient = 2 M1 (indep) attempt to subs x=3, y=4 into any linear equation A1 for y = 2x – 2 SC B2 for 2x–2
3
[5]
16.
(a)
–4 = 2a – 3 where a is the required x coordinate 1 – 2 1 M1 for –4 = 2a – 3 or x shown as 2
2
1 1 A1 – 2 or (– 2 , –4) (b)
y = 2x + c 4 = 2 × 3 + c, c = –2 y = 2x – 2 M1 for y = 2x + c (c ≠ –3) or gradient = 2 M1 (indep) attempt to subs x=3, y=4 into any linear equation A1 for y = 2x – 2 SC B2 for 2x–2
y=3–
(c)
1 x 2
3
1 B1 cao [6]
17.
(i)
5/3 oe
2 B1 (accept 1.66/7)
(ii)
−2
B1 cao [2]
18.
−2 5 oe 3 2 − x y= 5 5
2
−2 B1 for y = 5 x + constant −2 B1 ft for gradient “ 5 ” [2]
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19.
(a)
8
2
5 = 0.5 x + 1 M1 for 5 = 0.5 x + 1 A1 cao (b)
x = 2y – 2 oe
2 M1 for correctly multiplying both sides by 2 or correctly x isolating 2 y −1 A1 for x=2y − 2 oe or x = 0.5 oe SC: B1 for x = 2y − 1 [4]
20.
(a)
3
2
6 5 y= 2x+ 2 6 M1 for y = 2 x + constant A1 for 3 [SC: B1 ft from y = ax + b for m = a] (b)
7 6 oe
2
12 – 6k = 5 M1 for substitution of y = 6 into given equation or their rearrangement of it. A1 cao [4]
21.
(a)
–3
1 B1 cao
(b)
0, 5
1 B1 cao [2]
22.
S, P, R, Q
2 B2 all correct (B1 for 2 or 3 correct) [2]
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