Question

Find an equation of a line containing the points (-6,1) and (2,-5). 

Answer 1

y = - $\frac{3}{4}$ x  - $\frac{7}{2}$

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

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

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

the partial equation is

y = - $\frac{3}{4}$ x + c

to find c substitute either of the 2 given points into the partial equation

using (- 6, 1 ), then

1 = $\frac{9}{2}$ + c ⇒ c = 1 - $\frac{9}{2}$ = - $\frac{7}{2}$

y = - $\frac{3}{4}$ x - $\frac{7}{2}$ ← equation of line