Question

1. What is the slope of the line in the graph shown below?

2. Fine the slope that passes through (-2, -3) and (1, 1).
A. 1/3
B. 1
C. 2
D. 4/3

3. For the equation -4y=8x, what is the constant of variation?
A. -4
B. -2
C. 1
D. 2

Answer 1

1. Answer( -2)
2. Answer is D. 4/3
3. Answer is either A or B

Answer 2

Answer:

1). Slope of line = -2.

2). Option D is correct.i.e., $Slope=\frac{4}{3}$

3). Option B is correct.i.e., constant of variation is -2.

Step-by-step explanation:

1).

Given: A line and its two points in graph

To find: Slope of line in graph

Formula used to find Slope from two points is given by,

$Slope\:of\:line=\:\frac{y_2-y_1}{x_2-x_1}$

Points are ( 0 , 3 ) , ( 1 , 1 )

$Slope\:=\:\frac{1-3}{1-0}\\\\Slope\:=\:\frac{-2}{1}\\\\\implies Slope=\:-2$

Therefore, Slope of line = -2.

2).

Given: Points ( -2 , -3 ) & ( 1 , 1 )

To find: Slope of line which passes through given points.

We again use formula of Slope from two points,

$Slope\:=\,\frac{y_2-y_1}{x_2-x_1}\\\\Slope\:=\,\frac{1-(-3)}{1-(-2)}\\\\Slope\:=\,\frac{1+3}{1+2}\\\\Slope\;=\,\frac{4}{3}$

Therefore Option D is correct.i.e., $Slope=\frac{4}{3}$

3).

Given: equation , -4y = 8 x

To find: Constant of variation

The constant of variation is the relationship between variables that does not changes

Consider,

-4y = 8x

Transpose -4 to RHS

$y=\frac{8x}{-4}$

y = -2x

So, if we put any value of x we get value of y which is -2 times value of x.

⇒ Constant of variation is -2

Therefore, Option B is correct.i.e., constant of variation is -2.