Find the main equation of the line in the following cases 5 STARS?

1.
Equation of the straight line :
(y - 8) / (x - 3) = -1
y - 8 = -(x - 3)
y - 8 = -x + 3
x + y - 11 = 0

2.
Equation of the straight line :
(y - 3) / (x - 4) = (-3 - 3) / (0 - 4)
(y - 3) / (x - 4) = 3 / 2
3 (x - 4) = 2 (y - 3)
3x - 12 = 2y - 6
3x - 2y - 6 = 0

1.
y = -x + b
8 = -3 + b
b = 8 + 3 = 11
y = -x + 11

2.
Slope = rise/run = (-3 - 3) / (0 - 4) = (-6)/(-4) = 1.5
y = 1.5x + b
-3 = 1.5*0 + b
-3 = 0 + b
b = -3
y = 1.5x - 3

If you have the coordinates of a point and the slope of the line, you can write the equation in point-slope form, then convert it to other forms.

Point-slope equation for line of slope m that passes through (x₀,y₀):
y - y₀ = m(x - x₀)

Point-slope equation for line of slope -1 that passes through (3,8):
y - 8 = -1(x - 3)

Slope-intercept equation for the line:
y = -x + 11

Standard-form equation
x + y = 11

The typical equation of a line is: y = mx + b → where m: slope and where b: y-intercept

y = mx + b → given that the slope is: m = - 1

y = - x + b


The line passes through A (3 ; 8), so the coordinates of this point must verify the equation of the line.

y = - x + b

b = y + x → you substitute x and y by the coordinates of the point A (3 ; 8)

b = 8 + 3

b = 11

→ The equation of the line is: y = - x + 11

x + y = 11