m = [tex]\frac{5}{6}[/tex] , y - 7 = [tex]\frac{5}{6}[/tex] ( x - 12), y = [tex]\frac{5}{6}[/tex] 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 = [tex]\frac{7+8}{12+6}[/tex] = [tex]\frac{15}{18}[/tex] = [tex]\frac{5}{6}[/tex]
(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 = [tex]\frac{5}{6}[/tex] and (a , b) = (12, 7 )
y - 7 = [tex]\frac{5}{6}[/tex] (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 = [tex]\frac{5}{6}[/tex] - 10
y = [tex]\frac{5}{6}[/tex] x - 3
