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

1). Slope of line = -2.

2). Option D is correct.i.e.,
`Slope=(4)/(3)`

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

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=\:(y_2-y_1)/(x_2-x_1)`

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

`Slope\:=\:(1-3)/(1-0)\\\\Slope\:=\:(-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\:=\,(y_2-y_1)/(x_2-x_1)\\\\Slope\:=\,(1-(-3))/(1-(-2))\\\\Slope\:=\,(1+3)/(1+2)\\\\Slope\;=\,(4)/(3)`

Therefore Option D is correct.i.e.,
`Slope=(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=(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.