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

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.  

Answer 2

Answer:

The slope  of the line that passes through the pair of points (1, 7) and (10, 1) is    $\frac{-2}{3}$

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  $\frac{-33}{16}$

Step-by-step explanation:

Formula of slope of line (m) : $\frac{y_2-y_1}{x_2-x_1}$

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) $=\frac{1-7}{10-1}$

                $=\frac{-6}{9}$

                 $=\frac{-2}{3}$

Thus the slope  of the line that passes through the pair of points (1, 7) and (10, 1) is    $\frac{-2}{3}$

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) $=\frac{3.1-6.1}{-2.5-(-5.5)}$

                $=\frac{-3}{3}$

                 $= -1$

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) $=\frac{\frac{5}{2}-(-3)}{-5-(\frac{-7}{3})}$

                $=\frac{\frac{5}{2}+3}{-5+\frac{7}{3}}$

                $=\frac{-33}{16}$

Thus the slope of the line that passes through the pair of points (-7/3, -3) and (-5, 5/2) is  $\frac{-33}{16}$