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Answer:
Write down the gradient of each of these lines.
(a) y = 3x + 1 (b) y = 2x − 5 (c) y = 7x + 4 (d) y = 10x + 5
(e) y = x − 2 (f) y = 6x (g) y = −4x + 3 (h) y = −3x − 7
(i) (j)
Write down where each of these lines cross the y-axis (y-intercept)
(a) y = 2x + 3 (b) y = 7x + 1 (c) y = 3x − 2 (d) y = x − 5
(e) y = 2x (f) y = −4x + 6 (g) y = −5x − 3 (h) y = −3x
(i) (j)
Write down the equation of the lines below
(a) gradient of 3 and y−intercept of 6 (b) gradient of 2 and y−intercept of −1
(c) gradient of −4 and y−intercept of 3 (d) gradient of 8 and y−intercept of 4
(e) gradient of 1 and passing though (0, 4) (f) passing through (0, −2) with gradient 4
(g) gradient of −5 and passing through the origin.
(a) Does the point (2, 5) lie on the line y = 3x − 1 ?
(b) Does the point (4, 1) lie on the line y = 3x + 1 ?
(c) Does the point (3, 1) lie on the line y = x − 3 ?
(d) Does the point (5, 7) lie on the line y = −3x + 22 ?
(e) Does the point (−4, −8) lie on the line y = −2x ?
(f) Does the point (−1, 8) lie on the line y = 2x + 11 ?
(g) Does the point (12, 60) lie on the line y = 7x − 18 ?
Step-by-step explanation:
point (5, −2) lies on which lines below
Do the points (1, 4), (4, 10) and (9, 20) lie in a straight line?
Question 3: A line has equation y = 2x + 6
The line crosses the x−axis at the point A
The line crosses the y−axis at the point B
The point C has coordinates (1, 8)
(a) Find the coordinates of the point A
(b) Find the coordinates of the point B
(c) Find the equation of the straight line passing through the points A and C. Do the lines y = 3x + 1 and 4x − 2y + 3 = 0 have the same gradients?
Question 5: Line 1 has equation y = 3x − 12
(a) Find the coordinates of P
(b) Find the equation of Line 2
Lexi says the line below has an
equation of y = −2x +8
Explain her mistake.
Given: A graph showing intersection of two lines
To Find : Solution of the system
Solution:
Pair of linear equations
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Consistent
if a₁/a₂ ≠ b₁/b₂ (unique solution and lines intersects each others)
a₁/a₂ = b₁/b₂ = c₁/c₂ (infinite solutions and line coincide each other )
Inconsistent
if a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ( No solution , lines are parallel to each other)
in this case lines are intersecting
Hence solution of the system is unique
and is intersection point
from the graph intersection point is ( 2 , 0)
Hence solution is x = 2 and y = 0
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