More angles? More Spain- without the S. Anyway here we go!
1 answer:
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Answer:
a. y = -1/2x - 2
Step-by-step explanation:
The correct answer choice can be determined by finding the slope of the line. The slope is the ratio of rise to run.
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<h3>slope</h3>The x-intercept is 4 units left of the y-axis. As the line "runs" those 4 units, it "rises" -2 units to intercept the y-axis at -2. The slope of the line is ...
m = rise/run = -2/4 = -1/2
In the slope-intercept form of the equation of a line, the slope is the coefficient of x. This information is sufficient to let us choose the first answer choice.
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<h3>equation</h3>The slope-intercept equation is ...
y = mx +b . . . . . . . slope m, y-intercept b
We know the slope is -1/2, and the y-intercept is where x=0, at y=-2. Then the equation is ...
y = -1/2x -2 . . . . . matches choice A
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<em>Additional comment</em>
When answering multiple-choice questions, you only need to do enough work to tell which answers are <em>not</em> viable.
When we plot the points, we see that the line has negative slope. (eliminates choice C). The slope is shallow, rather than steep (the x-intercept is farther from the origin than the y-intercept), so the magnitude of the slope is less than 1 and choices B and D are eliminated.
➻ In a group of 40 people, 27 can speak English and 25 can speak Spanish.
➻ The required number of people who can speak both English and Spanish .
<u>Consider</u> ,
➻ A → Set of people who speak English.
➻ B → Set of people who speak Spanish
➻ A∩B → Set of people who can speak both English and Spanish
- ➻ n (A) = 27
- ➻ n (B) = 25
- ➻ n (A∪B) = 40
- ➻ n(A∩B) = ?
➻ n(A∪B) = n(A) + n (B) - n(A∩B)
➻ 40 = 27 + 25 - n (A∩B)
➻ 40 = 52 - n (A∩B)
➻ n (A∩B) = 52 - 40
➻ ∴ n (A∩B) = 12
∴ Required Number of persons who can speak both English and Spanish are <u>12 .</u>
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➻ n(A∪B) = n(A) + n (B) - n(A∩B)
➻ 40 = 27 + 25 - 12
➻ 40 = 52 - 12
➻ 40 = 40
➻ ∴ L.H.S = R.H.S
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