Complete the solution of the equation. Find the value of y when x equals -4. x + 3y = 14
1 answer:
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Answer: By the slope formula.
Step-by-step explanation:
Given: ABC is a triangle (shown below),
In which A≡(6,8), B≡(2,2) and C≡(8,4)
And, D and E are the mid points of the line segments AB and BC respectively.
Prove: DE║AC and DE = AC/2
Proof:
Since, And, D and E are the mid points of the line segments AB and BC respectively.
Therefore, By mid point theorem,
coordinate of D are
Coordinate of E are
By the distance formula,
By the slope formula,
Slope of AC =
Slope of DE =
Statement Reason
1. The coordinate of D are (4,5) and 1. By the midpoint formula
the coordinate of E are (5,3)
2. The length of DE = √5 2. By the Distance formula
The length AC = 2√5 ⇒ Segment DE
is half the length of segment AC
3. The slope of DE = -2 and the 3. By the slope formula
slope of AC = -2
4. DE║AC 4. Slopes of parallel lines are equal
Answer:
(a) y = -4x + 4 (b) y = 2x + 3
<u>solving steps:</u>
note: m refers to slope and y₁ to y point and x₁ to x point
a)
coordinates: (2,-4)
slope: -4
equation:
- y - y₁ = m(x - x₁)
- y - -4 = -4(x-2)
- y = -4x + 8 - 4
- y = - 4x + 4
b)
coordinates: (1,5), (-1,1)
slope:
- 2
equation:
- y - y₁ = m(x - x₁)
- y - 5 = 2(x - 1)
- y - 5 = 2x - 2
- y = 2x - 2 + 5
- y = 2x + 3