Answer:
y = - 3x + 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m =
with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (5, - 8)
m = =
= - 3 , thus
y = - 3x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (2, 1) , then
1 = - 6 + c ⇒ c = 1 + 6 = 7
y = - 3x + 7 ← equation of line
Point B on the ground is 5 cm from point E at the entrance to Ollie's house.
Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.
The complete question is as follows:
Ollie has installed security lights on the side of his house that is activated by a sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m, and the distance from B to C is 6m. Angle ACB is 15°.
The objective of this information is:
The diagrammatic representation of the information given is shown in the image attached below.
Using cosine rule to determine angle CAB, we have:
Here:
∠CAB = Sin⁻¹ (0.3451)
∠CAB = 20.19⁰
From the diagram attached;
Then, we can say:
∠CBD = ∠GBF
∠GBF = (CAB + ACB)
(because the exterior angles of a Δ is the sum of the two interior angles.
∠GBF = 15° + 20.19°
∠GBF = 35.19°
Using the trigonometric function for the tangent of an angle.
BF = 2.55 m
Finally, the distance of Ollie║FE║ from the entrance of his bouse is:
= 5 - 2.55 m
= 2.45 m
Therefore, we can conclude that Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.
Learn more about exterior angles here:
