Question

Cada par de puntos determina una recta con la pendiente dada. Halla el valor de la incógnita en cada caso: a. (3,2);(4,x); m=1 b. (b,-1);(2,-2); m=-1/2 c. (5,d);(9,2); m=-3/4 d. (-1/3,3/4);(h,5/6); m=7/12

Answer 1

a=3,b=0,c=5,d=-4/21

Explanation:

The formule we use to get the slope is:

m =
`(y2-y1)/(x2-x1)`

a. (3,2);(4,x); m=1

`(x-2)/(4-3)=1` → x= (1)(4-3)+2 → 3

b. (b,-1);(2,-2); m=-1/2

`(-2-(-1))/(2-b)=(-1)/(2)` → -1= (
`(-1)/(2)`)(2-b) →
`(-1)/((-1)/(2) )-2` → 0

c. (5,d);(9,2); m=-3/4

`(2-d)/(9-5)=(3)/(4)` → d= (
`(-3)/(4)`)(9-5)-2 → 5

d. (-1/3,3/4);(h,5/6); m=7/12

`((5)/(6)-(3)/(4) )/(h-(-1)/(3) )=(7)/(12)` →
`(5)/(6)-(3)/(4)`=
`(7)/(12)` (
`{h-(-1)/(3) }`) →
`(-4)/(21)`

We get this equation with the original one:

y=mx+b

There are three forms of linear equations:

point-slope form y2-y1=m(x2-x1)

standard form Ax + By + C = 0 or Ax + By = C

and slope-intercept form y=mx+b