Question

(PICTURE) Which equation is a point slope form equation for line AB ?

Answer 1

The last one : y - 5 = $\frac{3}{4}$(x - 6)

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = A(- 2, - 1 ) and (x₂, y₂ ) = (B(6, 5 )

m = $\frac{5+1}{6+2}$ = $\frac{6}{8}$ = $\frac{3}{4}$

using (a, b ) = (6, 5 ), then

y - 5 = $\frac{3}{4}$(x - 6 ) ← in point- slope form