Question

What is an equation of the line that passes through the points (0, -2) and (−5,4)? Put your answer in fully reduced form.

Answer 1

The equation of the line is y =
`-(6)/(5)` x - 2 OR 6x + 5y = -10

Explanation:

The form of the linear equation is y = m x + b, where

• m is the slope

• b is the y-intercept ⇒ value y at x = 0

The rule of the slope of a line is

• m =
  `(y2-y1)/(x2-x1)`

• (x1, y1) and (x2, y2) are two points lie on the line

→ Let us solve the question

∵ The line passes the points (0, -2) and R (-5, 4)

∴ x1 = 0 and y1 = -2

∴ x2 = -5 and y2 = 4

→ Substitute them in the rule of the slope above to find it

∵ m =
`(4--2)/(-5-0)=(4+2)/(-5)=-(6)/(5)`

∴ m =
`-(6)/(5)`

Substitute it in the form of the equation above

∴ y =
`-(6)/(5)` x + b

∵ b is the y-intercept (value y at x = 0)

∵ At x = 0, y = -2

∴ b = -2

→ Substitute it in the equation

∴ y =
`-(6)/(5)` x + (-2)

→ Remember (+)(-) = (-)

∴ y =
`-(6)/(5)` x - 2

→ Multiply both side by 5 to cancel the denominator of the fraction

∴ 5y = -6x - 10

→ Add 6x to both sides

∴ 6x + 5y = -6x + 6x - 10

∴ 6x + 5y = -10

∴ The equation of the line is y =
`-(6)/(5)` x - 2 OR 6x + 5y = -10