Question

What is the equation for this line?

Answer 1

The equation of the line is y = 2x - 3

Explanation:

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

• m is the slope of the line,
  `m=(y2-y1)/(x2-x1)`

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

Let us take two points on the line to find its equation

∵ Points (3, 3) and (0, -3) lie on the line

∴ x1 = 3 and y1 = 3

∴ x2 = 0 and y2 = -3

→ Use the rule of the slope above to find m

∵
`m=(-3-3)/(0-3)=(-6)/(-3)=2`

∴ m = 2

→ Substitute its value in the form of the equation above

∴ y = 2x + b

∵ b is the value of y at x = 0

∵ y = -3 at x = 0

∴ b = -3

→ Substitute it in the equation above

∴ y = 2x + -3

→ Remember (+)(-) = (-)

∴ y = 2x - 3

∴ The equation of the line is y = 2x - 3