Can some one help me with these math problems?

Question

Write an equation of a line in y=mx+b form, that contains a slope of -1/5 and passes through(10, 7)

Write an equation of a line in y=mx+b fpm, that passes through the points (1, -4) and (-1,6)

Write an equation of a line in y=mx+b form that contains the following point(6,-5) and is parallel to its given line y=1/2x-3

Write an equation in y=mx+b form that contains the following point (20,7) and is perpendicular to its given line, y=-5x=11

Thanx a BUNCH!!!!

**KIA**

Answer 1

a) m = -1/5, so the equation will be y = -1/5 x + b for some b. Put in (10, 7) and we get 7 = -1/5 (10) + b => b = 7 + 2 = 9. So the line is y = -1/5 x + 9.

b) m = (y2-y1)/(x2-x1) = (6 - (-4)) / (-1 - 1) = 10/(-2) = -5. So y = -5x + b, put in (1, -4) and we get -4 = -5 + b, so b = 1. So the line is y = -5x + 1.

c) Parallel to y = 1/2 x - 3 => line is y = 1/2 x + b for some b. Put in (6, -5) and we get -5 = 1/2 (6) + b => b = -8, so the line is y = 1/2 x - 8.

d) Perpendicular to y = -5x - 11: gradient of y = -5x - 11 is -5, so a perpendicular line will have gradient -1 / (-5) = 1/5. So the line is y = 1/5 x + b for some b, put in (20, 7) and we get 7 = 1/5 (20) + b => b = 3. So the line is y = 1/5 x + 3.

Answer 2

Write an equation of a line in y=mx+b form, that contains a slope of -1/5 and passes through(10, 7)

7=(-1/5)(10) +b
7= -2 + b
9=b

y=(-1/5)x + 9

Write an equation of a line in y=mx+b fpm, that passes through the points (1, -4) and (-1,6)

find slope using y-y/x-x
-4-6/1- -1
-10/2
-5

y= -5x+b

then sub in a point to get b
-4=-5(1)+b
1=b

y= -5x+1

Write an equation of a line in y=mx+b form that contains the following point(6,-5) and is parallel to its given line y=1/2x-3

when its parallel it has the same slope so use the slop 1/2 and plug in the point

-5=1/2(6) +b
-5=3+b
-8=b

y=1/2x-8

Write an equation in y=mx+b form that contains the following point (20,7) and is perpendicular to its given line, y=-5x=11

perpendicular lines have NEGATIVE RECIPRICOL slopes... so u flip it and change the sign... so the slope will be 1/5.. plug in the point

7=1/5(20)+b
7=4+b
3=b

y= 1/5+3

Answer 3

y=-1/5x+7

that's the first one.