Question

If y varies directly as x andx = 12 when y = 24, what is x when y = 8? (I just need to know the rate of change, y-intercept, x-intercept, what m & b are, & what the equation is in slope-intercept form.)

Answer 1

If y varies directly as x and x = 12 when y = 24, what is x when y = 8.?

So, y = c * x

where c is constant

x = 12 when y = 24

so,

24 = c * 12

c = 24/12 = 2

so,

y = 2x

Now, need to find x when y = 8

so,

8 = 2x

x = 8/2 = 4

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From the graph:

y-intercept = 3 , it is the value of y when x = 0

the general form of the line: y = mx + b

where b is y-intercept

So, y = mx + 3

to find m, choose point like (2 , 2) and substitute with it

so, y = 2 when x =2

2 = 2m + 3

2m = -1

m = -1/2 = -0.5

so, y = -0.5x + 3

so, to find x-intercept is the value of x when y = 0

so, 0 = -0.5x + 3

0.5x = 3

x = 3/0.5 = 6

m is the slope = -0.5

b is y-intrcept = 3