Question

What is an equation of the line that passes through the points (-1, -6) and (6, 1)?

Answer 1

y = x - 5.

Explanation:

Slope of the line

= (1 - -6) / (6 - -1)

= 7/7

= 1

y - y1 = m(x - x1)

m = 1 and (x1, y1) = (6, 1) so,

y - 1 = 1(x - 6)

y = x - 6 + 1

y = x - 5.

We could have used (x1, y1) = (-1, -6) .We would have obtained the same result.

Answer 2

Explanation:

It is vital to first find the gradient/ slope between the points

`m=(y2-y1)/(x2-x1) \\=(1-(-6))/(6-(-1))\\ \\m=1`

let us use the point (6,1) to find the value of c

y=mx+c

1=1(6)+c

1-6=c

∴c=-5

the equation is given by

y=x-5