Question

Find the equation of the straight line passing through A(10,-2) and B(4,1)

Answer 1

y = -
`(1)/(2)` x + 3

Explanation:

The equation of a line in slope- intercept form is

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

Calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = A(10, - 2) and (x₂, y₂ ) = B(4, 1)

m =
`(1+2)/(4-10)` =
`(3)/(-6)` = -
`(1)/(2)` , then

y = -
`(1)/(2)` x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 1 )

1 = - 2 + c ⇒ c = 1 + 2 = 3

y = -
`(1)/(2)` x + 3 ← equation of line