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weeeeeb [17]
3 years ago
11

1.

Mathematics
2 answers:
Anna007 [38]3 years ago
5 0

Answer:

1) The correct option is C. (2) The correct option is D. (3) The correct option is B. (4) The correct option is D. (5) The correct option is D.

Step-by-step explanation:

The slope formula is

m=\frac{y_2-y_1}{x_2-x_1}

(1)

Two points are (-2,5) and (1,4).

m=\frac{4-5}{1-(-2)}=\frac{-1}{3}tex]Therefore option C is correct.(2)Use the above mentioned formula for each pair of coordinates.[tex]m=\frac{10-13}{17-12}=\frac{-3}{5}

m=\frac{10-15}{13-16}=\frac{-5}{-3}=\frac{5}{3}

m=\frac{10-7}{3-0}=\frac{3}{3}=1

m=\frac{18-13}{8-11}=\frac{5}{-3}=\frac{-5}{3}

Therefore option D is correct.

(3)

The pair of points (6, y) and (10, -1). The slope is \frac{1}{4}.

\frac{1}{4}=\frac{-1-y}{10-6}

\frac{1}{4}=\frac{-1-y}{4}

1=-1-y

y=-2

Therefore option B is correct.

(4)

For vertical line the x coordinates always remains the same. Therefore when we subtract the same number we get zero in the denominator, therefore the value of slope is undefined for a vertical line.

Therefore option D is correct.

(5)

Two points from the table are (2,110) and (3,165).

m=\frac{165-110}{3-2}=\frac{55}{1}

Therefore option D is correct.

Tanya [424]3 years ago
4 0

Answer:

For 1: The correct option is C.

For 2: The correct option is D.

For 3: The correct option is B.

For 4: the correct option is D.

For 5: The correct option is D.

Step-by-step explanation:

  • For 1:

To calculate the slope of a line formed by two points, we use the formula:

Slope=\frac{y_2-y_1}{x_2-x_1}     ....(1)

Points given are (-2,5) and (1,4)

Slope=\frac[4-5}{1-(-2)}=\frac{-1}{3}

Hence, the correct option is C.

  • For 2:

Using equation 1, we calculate the slopes for every options, we get:

Option A: Points are (12,13) and (17,10)

Slope=\frac{10-13}{17-12}=\frac{-3}{5}

Option B: Points are (16,15) and (13,10)

Slope=\frac{10-15}{13-16}=\frac{-5}{-3}=\frac{5}{3}

Option C: Points are (0,7) and (3,10)

Slope=\frac{10-7}{3-0}=\frac{3}{3}=1

Option D: Points are (11,13) and (8,18)

Slope=\frac{18-13}{8-11}=\frac{5}{-3}=\frac{-5}{3}

Hence, the correct option is D.

  • For 3:

We are given two points (6,y) and (10,-1) and the slope of the line is \frac{1}{4}

Using equation 1, we get

\frac{1}{4}=\frac{-1-y}{10-6}

\frac{-1-y}{4}=\frac{1}{4}

-1-y=1\\y=-2

Hence, the correct option is B.

  • For 4:

The slope of any line is \tan\theta, where \theta is the angle made by the line with the positive x-axis in counter-clockwise direction.

So, the vertical line will form 90° with x-axis and hence, \theta =90^o

As, \tan90^o=\infty

Hence, the correct option is D.

  • For 5:

The given data is forming a linear relation. So, the slope will be same throughout its entire length.

The points taken for the calculation of slope are (2,110) and (3,165)

Slope=\frac{165-110}{3-2}=\frac{55}{1}

Hence, the correct option is D.

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