1. C(4,4) , D(-2,-8)

#1) find the slope of the line that passes through each pair of points

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1. (-8-4)/(-2-4) = 2

2. y= mx +b, where m is slope and b is y intercept, so the slope is -2 and the y intercept is zero.

3. for a function to be linear all variables must be to the first power, and since both of the equations have x and y to the first power( meaning that it is just x, rather than x squared) then the functions are linear and fit the for y = mx + b

a) y = (3/4)x + 0

b) -(3/2)x + 6

1. The slope of the line which passes through points C and D could be found using the formula:

(YD-YC)/(XD-XC), where

YD=-8; YC=4

XD=-2; XC=4, so

(-8-4)/(-2-4)=2

2. The explicit equation of a line, given by the slope and the ordinate at origin is:

y=mx + n , where m-slope and n-odinate at origin

In this case, the equation is *y=-2x.*

So, from these two equations, it results the next statement:

-2x=mx + n

Two expressions are equivalent, if all the terms from the left side of equal sign are the same with all the terms from the right side of the equal sign, so:

m=-2 and n=0

3. Taking account of the explicit equation of a line:

y=mx + n,

We are trying to put both equations in this form:

a) *y=3/4 x, is a linear function, because the two variables,x and y, are at first power and m=3/4 and n=0*

b) *y=-3/2 x + 6, also a liner function, regarding what I've said at a), and m=-3/ and n=6*

1) Use the formula y2-y1 and divide by x2-x1 therefore -8-4 = -12 and -2 - 4 = -6 then you take -12 and divide by -6 and your slope = 2. You could double check this by graphing the two points and use rise over run to see if it rises two and runs one from one point to the next.

2) The slope is -2 (which is always the number with the x) and the y-intercept would be 0 because there is nothing listed with the -2x. Your graph would cross through the origin.

3) Y = 3/4x is linear. you can check by picking a set of values for x. if x = -1, then y would equal = 3/4, if x = 0 then y would equal 0. if x = 1, then y would equal 3/4. these would connect in a straight line. The line increases 3/4 for each step. The second equation 3x + 2y = 12 can been seen in slope intercept form as 2y= -3x + 12, then divide everything by 2 and you would get y = -3/2x + 6. This would also be graphed as a straight line with a slope of -3/2 and a y-intercept of 6.

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

m=(4+8)/(4+2)

m=12/6

m=2

Use the slope formula m = -b/a. Hope this link will help you.

Since gradient, m = (y2-y1)/ (x2-x1)

m= (-8-4)/ (-2-4)

= (-12)/(-6) = 2 unita

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