Answer:
Step-by-step explanation:
Factorise the denominator of the second fraction
y² - 1 = (y - 1)(y + 1) ← difference of squares
To obtain a common denominator
multiply numerator/ denominator of first fraction by (y + 1)
= -
← subtract numerators leaving the common denominator
=
=
= ← cancel common factor (y - 1) on numerator/denominator
=
m = , y - 7 =
( x - 12), y =
x - 3
(a) calculate the slope using the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 6, - 8) and (x₂, y₂) = (12, 7)
m = =
=
(b) the equation of a line in point-slope form is
y - b = m(x - a )
where m is the slope and (a, b) a point on the line
using m = and (a , b) = (12, 7 )
y - 7 = (x - 12)
(c) the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange (b ) into this form
y - 7 = - 10
y = x - 3
