Answers:
_________________________________________________1) "
y = - x – 5 " .
_______________________________________2) "
y = -2x + 2 "
_______________________________________
3) y = "
x + " .
_______________________________________
Explanation:_______________________________________1) "
y = -x<span>
– 5 " .
Note: This equation is in the "slope-intercept form" ; that is:
" y = mx + b" ; in which: the slope, "m = -1 " ;
the y-intercept, "b = -5 " .
_______________________________________ </span>1) y = -x – 5 ;
Note: This equation is in the "slope-intercept form" ; that is:
" y = mx + b" ; in which: the slope, "m = -1 " ;
the y-intercept, "b = -5 " .
_______________________________________2) "
y = -2x + 2 " .
Note: Given: "(x₁, y₁)" ; that is: "(-2, 6)" ; in which: "x₁ = -2" ; and: "y₁ =6" ;
And given the slope, "m", = -2 ;
Use the formula:
" y – y₁ = m(x – x₁) " ;
And substitute our known values:
" y – 6 = -2 [x – (-2)] " ;
→ " y – 6 = -2 (x + 2) ;
→ " y – 6 = (-2*x) + (-2*2) ;
→ " y – 6 = (-2*x) + (-2*2) ;
→ " y – 6 = -2x + (-4) ;
→ " y – 6 = -2x – 4 ;
→ Now, add "6" to EACH SIDE of the equation; to isolate "y" on the
"left-hand side" of the equation; & write in "slope-intercept form" ;
→ " y – 6 + 6 = -2x – 4 + 6 ;
to get:
→ "
y = -2x + 2 " .
Note: This equation is in the "slope-intercept form" ; that is:
" y = mx + b" ; in which: the slope, "m = -2 " ;
the y-intercept, "b = 2 " .
_______________________________________3) "
y = x + " .
Given the points: "(-1, 1)" ; and "(7, 15):
→ "(x₁, y₁)" ↔ "(-1, 1)" ; in which: " x₁ = -1 " ; " y₁ = 1 " ;
→ "(x₂ , y₂)" ↔ "(7, 15)" ; in which: " x₂ = 7 " ; "y
₂ = 15 " ;
______________________________________________
Calculate the slope, "m" :
→ m = (
y
₂ – y₁) / (x₂ – x₁) ;
= (15 – 1) / [ 7 – (-1) ] = (15 – 1) / ( 7 + 1) ;
=
;
_______________________________________________
→ Now, use the formula:
→ " y – y₁ = m(x – x₁) " ;
And substitute our known values:
→ " y – 1 =
[x – (-1)] " ;
→ " y – 1 =
(x + 1) " ;
→ " y – 1 =
x +
" ;
→ Now, add "1" to EACH SIDE of the equation; to isolate "y" on the
"left-hand side" of the equation; & write in "slope-intercept form" ;
→ " y – 1 + 1 =
x +
+ 1 " ;
to get:
→ "
y = x + " .
And substitute our known values:
Note: This equation is in the "slope-intercept form" ; that is:
" y = mx + b" ; in which: the slope, "m =
" ;
the y-intercept, "b =
" .
_____________________________________________________