Question

What is the slope of the line that passes throught the pair of points (1, 7) and (10, 1)?

a. 3/2
b. -2/3
c. -3/2
d. 2/3

8. What is the slope of the line that passes through the points (-5.5, 6.1) and (-2.5, 3.1)?

a. -1
b. 1
c. -3
d. d

9. what is the slope of the line that passes through the pair of points (-7/3, -3) and (-5, 5/2)?

a. 6/22
b. -6/22
c. 22/6
d. -22/6

Answer 1

The slope of the line that passes through the pair of points (1, 7) and (10, 1) is
`(-2)/(3)`

The slope of the line that passes through the points (-5.5, 6.1) and (-2.5, 3.1) is -1

The slope of the line that passes through the pair of points (-7/3, -3) and (-5, 5/2) is
`(-33)/(16)`

Explanation:

Formula of slope of line (m) :
`(y_2-y_1)/(x_2-x_1)`

Part 1 : Points are (1, 7) and (10, 1)

`(x_1,y_1) =(1,7)`

`(x_2,y_2) =(10,1)`

So, using formula

Slope (m)
`=(1-7)/(10-1)`

`=(-6)/(9)`

`=(-2)/(3)`

Thus the slope of the line that passes through the pair of points (1, 7) and (10, 1) is
`(-2)/(3)`

Part 2:Points (-5.5, 6.1) and (-2.5, 3.1)

`(x_1,y_1) =(-5.5,6.1)`

`(x_2,y_2) =(-2.5,3.1)`

So, using formula

Slope (m)
`=(3.1-6.1)/(-2.5-(-5.5))`

`=(-3)/(3)`

`= -1`

Thus the slope of the line that passes through the points (-5.5, 6.1) and (-2.5, 3.1) is -1

Part 3 : Points (-7/3, -3) and (-5, 5/2)

`(x_1,y_1) =(-7/3,-3)`

`(x_2,y_2) =(-5,5/2)`

So, using formula

Slope (m)
`=((5)/(2)-(-3))/(-5-((-7)/(3)))`

`=((5)/(2)+3)/(-5+(7)/(3))`

`=(-33)/(16)`

Thus the slope of the line that passes through the pair of points (-7/3, -3) and (-5, 5/2) is
`(-33)/(16)`

Answer 2

Answers
1) b. -2/3
2) a. -1
3) -33/16 (no correct answer from the choices)

Explanation
The slope of a line is simply the gradient.
The gradient is the ratio of change in y to change in x.
Gradient = (y2-y1)/(x2-x1)

Question 1
Slope =((7-1))/((1-10) )=6/(-9)=-2/3

Question 2
Slope = (6.1-3.1)/(-5.5—2.5)=3/(-3)=-1

Question 3
Slope = (5/2—3)/(-5—7/3)=(11/2)/(-8/3)=-33/16

For question 3, there is no correct answer.