:
question
the points (3,8) and (9,24) form a proportional relationship. find the slope of the line through the
points. then use the slope to graph the line.
the slope is

The answer is: the slope is 16/6. The line can be formed by plotting the two points and drawing a line between them, across the graph.

Step-by-step explanation:

The given points are:

(3, 8) and (9, 24)

m = (y - y1) / (x - x1)

m = 8 - 24 / 3 - 9

m = -16 / -6

m = 16/6

Use the Point slope version to find the y intercept version:

(y - y1) = m(x - x1)

y - 8 = 16/6(x - 3)

y - 8 = 16/6x - 16/6 * 3

y - 8 = 16/6x - 48/6

y - 8 = 16/6x - 8

y = 16/6x - 8 + 8

y = 16/6x - 0

y = 16/6x

Proof:

f(3) = 16/6 * 3 = 48/6 = 8

f(9) = 16/6 * 9 = 144/6 = 24

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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