Help linear equations...?

Question

Determine the slope of the line containing the points (6, -2) and (-1, 5).

Determine an equation for a line with slope ½ and y-intercept at (0, -3).

Determine an equation for a line parallel to y = -3x +4, containing the point

(2, 1).

Answer 1

1. 5 - (-2) / (-1) - 6 = -1

2. y = 1/2x - 3

3. y = -3x + 5

Just ask and I'll explain further...

Answer 2

[1] for reference: (x1,y1) = (6,-2) and (x2, y2) = (-1,5)

slope = m = change in y's divided by change in x's or (y2-y1)/(x2-x1) = (5-(-2))/(-1-6) = 7/(-7) = -1.  

Ans: the slope is -1.

[2] the equation of a line given its slope, m, and y-intercept, b, is just y=mx+b.  (0, -3) is a y-intercept of -3.

Ans: The equation of the line is y = (½ x)-3

[3] parallel lines have the same slope.  The slope of the line, which is presented in slope-intercept form y = -3x+4 can just be "read-off" as -3.  the equation of a line given its slope, m, and point (x1,y1) is y-y1=m(x-x1).  You're given (x1, y1) = (2,1).  Plugging the values in, you have y-1=-3(x-2).  combining like terms by keeping y terms on the left and all others on the right, distributing, you have y = -3x+6+1.

Ans: The equation is y = -3x+7

Answer 3

slope = (y2-y1)/(x2-x1) = (5--2)/(-1-6) = 7/-7 = -1

slope = ½ = m @ (0,-3)

y = mx + b

-3 =  ÃƒÂ‚½*0 + b

b = -3

y =  ÃƒÂ‚½x -3

parallel slope is same = m = -3

y = mx + b @ (2,1)

1 = -3*2 + b

1 = -6 + b --------> change sign on -6, move to the other side

1 + 6 = b

b = 7

y = -3x + 7