A-Level Maths Key Assignment 01 Linear Functions
,A-Level Maths Key Assignment 01 Linear Functions
ESSENTIAL INFORMATION for this Key Assignment
𝑦 is a linear function of 𝑥 if it can be expressed in the form 𝑦 = 𝑚𝑥 + 𝑐.
The graph of 𝑦 against 𝑥 is then a straight line, where 𝑚 is the gradient of the
line and 𝑐 is the value of 𝑦 when 𝑥 is zero and is the intercept on the 𝑦-axis.
A straight line of gradient 𝑚 passing through the point (𝑥! , 𝑦! ) has equation
𝑦 − 𝑦! = 𝑚(𝑥 − 𝑥! )
Lines that are parallel have the same gradient.
Two lines with gradients 𝑚! and 𝑚" are perpendicular if
𝑚! 𝑚" = −1
The mid-point of (𝑥! , 𝑦! ) and (𝑥" , 𝑦" ) is
𝑥! + 𝑥" 𝑦! + 𝑦"
, , .
2 2
The perpendicular bisector of two points 𝐴 and 𝐵 is the line that passes
through the midpoint of 𝐴 and 𝐵 and is perpendicular to 𝐴𝐵.
To determine where a line crosses the 𝑥-axis, substitute 𝑦 = 0 and solve the
resulting equation. To determine where a line crosses the 𝑦-axis, substitute
𝑥 = 0 and solve the resulting equation.
,A-Level Maths Key Assignment 01 Linear Functions
DAY ONE
1. Find the equation of the straight line passing through these points, in the
form 𝑦 = 𝑚𝑥 + 𝑐:
a. (0,3) and (2,7)
b. (1,4) and (2,6)
c. (5,4) and (10,19)
d. (1, −5) and (−4,0)
e. (1,2) and (−2,1)
f. (−3, −2) and (−1,2)
2. Determine the gradient of each of the following straight lines:
a. 𝑦 = 6𝑥 − 9
b. 𝑦 = 5 − 3𝑥
#$%&
c. 𝑦 =
"
d. 2𝑦 + 4𝑥 = 7
3. Rearrange the equation 12𝑥 − 9𝑦 = 11 into the form 𝑦 = 𝑚𝑥 + 𝑐, where
𝑚 and 𝑐 are rational numbers.
4. Which…
a. …of these lines are parallel to the line 𝑦 = 4𝑥 − 2?
i. 𝑦 = 2 − 4𝑥
ii. 𝑦 = 4𝑥 + 8
iii. 4𝑥 + 𝑦 + 6 = 0
iv. −8𝑥 + 2𝑦 − 7 = 0
b. …of these lines are parallel to the line 2𝑥 + 3𝑦 − 4 = 0?
i. 3𝑥 − 2𝑦 + 1 = 0
"
ii. 𝑦 = 𝑥 + 6
'
iii. 4𝑥 + 6𝑦 + 3 = 0
"
iv. 𝑦 = − 𝑥
'
, A-Level Maths Key Assignment 01 Linear Functions
5. Give the mid-point of each of these pairs of points.
a. (4,4) and (6,10)
b. (3,1) and (7,8)
c. (2,5) and (9,1)
d. (4, −2) and (8,4)
e. (−1,3) and (3, −1)
f. (−4,5) and (−1, −2)
,A-Level Maths Key Assignment 01 Linear Functions
ESSENTIAL INFORMATION for this Key Assignment
𝑦 is a linear function of 𝑥 if it can be expressed in the form 𝑦 = 𝑚𝑥 + 𝑐.
The graph of 𝑦 against 𝑥 is then a straight line, where 𝑚 is the gradient of the
line and 𝑐 is the value of 𝑦 when 𝑥 is zero and is the intercept on the 𝑦-axis.
A straight line of gradient 𝑚 passing through the point (𝑥! , 𝑦! ) has equation
𝑦 − 𝑦! = 𝑚(𝑥 − 𝑥! )
Lines that are parallel have the same gradient.
Two lines with gradients 𝑚! and 𝑚" are perpendicular if
𝑚! 𝑚" = −1
The mid-point of (𝑥! , 𝑦! ) and (𝑥" , 𝑦" ) is
𝑥! + 𝑥" 𝑦! + 𝑦"
, , .
2 2
The perpendicular bisector of two points 𝐴 and 𝐵 is the line that passes
through the midpoint of 𝐴 and 𝐵 and is perpendicular to 𝐴𝐵.
To determine where a line crosses the 𝑥-axis, substitute 𝑦 = 0 and solve the
resulting equation. To determine where a line crosses the 𝑦-axis, substitute
𝑥 = 0 and solve the resulting equation.
,A-Level Maths Key Assignment 01 Linear Functions
DAY ONE
1. Find the equation of the straight line passing through these points, in the
form 𝑦 = 𝑚𝑥 + 𝑐:
a. (0,3) and (2,7)
b. (1,4) and (2,6)
c. (5,4) and (10,19)
d. (1, −5) and (−4,0)
e. (1,2) and (−2,1)
f. (−3, −2) and (−1,2)
2. Determine the gradient of each of the following straight lines:
a. 𝑦 = 6𝑥 − 9
b. 𝑦 = 5 − 3𝑥
#$%&
c. 𝑦 =
"
d. 2𝑦 + 4𝑥 = 7
3. Rearrange the equation 12𝑥 − 9𝑦 = 11 into the form 𝑦 = 𝑚𝑥 + 𝑐, where
𝑚 and 𝑐 are rational numbers.
4. Which…
a. …of these lines are parallel to the line 𝑦 = 4𝑥 − 2?
i. 𝑦 = 2 − 4𝑥
ii. 𝑦 = 4𝑥 + 8
iii. 4𝑥 + 𝑦 + 6 = 0
iv. −8𝑥 + 2𝑦 − 7 = 0
b. …of these lines are parallel to the line 2𝑥 + 3𝑦 − 4 = 0?
i. 3𝑥 − 2𝑦 + 1 = 0
"
ii. 𝑦 = 𝑥 + 6
'
iii. 4𝑥 + 6𝑦 + 3 = 0
"
iv. 𝑦 = − 𝑥
'
, A-Level Maths Key Assignment 01 Linear Functions
5. Give the mid-point of each of these pairs of points.
a. (4,4) and (6,10)
b. (3,1) and (7,8)
c. (2,5) and (9,1)
d. (4, −2) and (8,4)
e. (−1,3) and (3, −1)
f. (−4,5) and (−1, −2)
