Question

1.
What is the slope of the line that passes through the points (-2,5) and (1,4)

A) -3
B) -2
C) -1/3
D) 1/3

2.
A line has a slope -5/3. Through which two points could this line pass?

A) (12,13), (17,10)
B) (16,15) ,(13,10)
C) (0,7), (3,10)
D) (11,13), (8,18)

3.
The pair of points (6, y) and (10, -1) lie on a line with the slope on 1/4. What is the value of Y?

A) -5
B) -2
C) 2
D) 5

4.
What is the slope with the vertical line?

A) -1
B) 0
C) 1
D) undefined

5.
The table below gives the cost per person to rent a fishing charter boat. Find the rate of change given that it is constant. Also, explaining the rate of change means for this situation. (The first photo)

A) 1/55
B) 110/1
C) 1/275
D) 55/1

Answer 1

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.

Answer 2

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.