Asap 15 points 1) find the slope of a line that contains (-4, 0) and (-6, -2). 2) find the slope of a line that contains (2, 8) and (1, -3). 3) the value of y varies directly with x, and y = 6 when x = 18. find y when x = 12. type your answer as an integer, like this: 58. 4) tell whether the equation represents a direct variation. if so identify the constant of variation. 32y = 96x a) yes, the constant of variation is negative 3 b) yes, the constant of variation is -1/3 c) no d) yes, the constant of variation is 3

Answers

1) 1

2) 11

3) 4

4) D) Yes, the constant of variation is 3

Explanation

Q1

The slope of a line is given by

Slope = (change in y)/(change in x)

= (0 - -2)/(-4 - -6)

= 2/2

= 1

Q2

Slope = Δy/Δx

= (8 - -3)/(2 - 1)

= 11/1

= 11

Q3

Y varies directly as X. This is written as,

Y ∞ X

Put and equal sign then introduce the constant of proportionality, K.

Y = KX

K = Y/X

K = 6/18 = 1/3

∴ Y = (1/3)X

Y = (1/3) × 12

Y = 4

Q4

32Y = 96X

Dividing both sides by 32,

Y = 96/32 X

Y = 3X

3 been the constant, Y varies directly as X.

So, the equation 32y = 96x is a direct variation.

Constant of variation = 3