Find the slope and the y-intercept of the graph of the linear equation. Then, graph the equation.
1 answer:
Answer:
The slope of the graph is: m = -6
The y-intercept of the graph is: b = 2
And the graph of the equation is shown below.
Step-by-step explanation:
We know that the slope-intercept form is
Where m is the slope and b is the y-intercept
Given the equation
comparing with the slope-intercept form
slope = m = -6
y-intercept = b = 2
Thus,
The slope of the graph is: m = -6
The y-intercept of the graph is: b = 2
And the graph of the equation is shown below.
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Answer:
Step-by-step explanation:
The given equation is expressed as
y = 1/(x - 2)
We will assume values for x and determine the corresponding values for y. Therefore,
When x = 0, y = 1/(0 - 2) = - 1/2
When x = 1, y = 1/(1 - 2) = - 1
When x = 2, y = 1/(2 - 2) = 0
When x = 3, y = 1/(3 - 2) = 1
When x = 4, y = 1/(4 - 2) = 1/2
To plot the graph, we would choose a suitable scale for the x and y axis of the graph.
Let 2 cm represent 1 unit on the vertical axis.
Let 2 cm represent 0.5 unit on the x axis.
The graph is shown in the attached photo
Answer:
θ = (60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = , so
θ = (
) =
( or 60° )