Question

Write the equation of the line that passes through the points

(3,-2) and (6, 1).
y=x-5
y = 5x + 1
y = -x + 5

Answer 1

It is y = x - 5

Explanation:

General equation of a line:

`{ \bf{y = mx + c}}`

m is the gradient, and c is y-intercept.

For gradient:

`slope = (y_(2) - y_(1) )/(x _(2) - x_(1))`

substitute:

`slope = (1 - ( - 2))/(6 - 3) \\ \\ = (3)/(3) \\ slope \: = 1`

m = 1

for y-intercept:

consider point (6, 1):

`y = mx + c \\ 1 = (6 * 1) + c \\ 1 = 6 + c \\ c = 1 - 6 = - 5`

therefore:

`{ \sf{equation \: is \: \{y = x - 5 \}}}`