Maths Straight Line

1.
(a)
y - 0 = (-4) (x - 0)
y = -4x
4x + y = 0

(b)
y - (-7) = (0) (x - 3)
y + 7 = 0
y = -7

(c)
perpendicular to the x-axis means parallel to the y-axis.
This is a vertical line passing through (4, 9)
That is, x = 4.

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2.
Slope = [1 - (-5)]/(-2 - 2) = 6/(-4) = -3/2
Equation is:
y - 1 = (-3/2)[x - (-2)]

y - 1 = (-3/2)(x + 2)
2y - 2 = -3x - 6
3x + 2y + 4 = 0

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3.
(a)
y-intercept = 4, that is, passes through (0, 4)
y - 4 = 7(x - 0)
y - 4 = 7x
y = 7x + 4
7x - y + 4 = 0

(b)
x-intercept = 4, that is, passes through (4, 0)
y - 0 = 3(x - 4)
y = 3x - 12
3x - y - 12 = 0

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4.
(a)
Slope of BA = (2 - 0)/(0 - 3) = -2/3
Equation of BA is
y - 0 = (-2/3)(x - 3)
3y = -2x + 6
2x + 3y - 6 = 0

Slope of CA = 2 × (Slope of BA) = 2 × (-2/3) = -4/3
Equation of CA is
y - 0 = (-4/3)(x - 3)
3y = -4x + 12
4x + 3y - 12 = 0

(b)
Using (a), put x = 0 in 4x + 3y - 12 = 0 to get
0 + 3y - 12 = 0
y = 4
Therefore, C = (0, 4)

(c)
Regard BC as the base, BC = 4 - 2 = 2
The height of triangle ABC is 3, observed from the x-coordinate of A.
The area of triangle ABC is
(1/2)(2)(3) = 3 sq. units.

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