Question

What is an equation of the line that passes through the points (-3, -2)(−3,−2) and (3, 6)(3,6)? Put your answer in fully reduced form.

Answer 1

The equation of the line is y =
`(4)/(3)` x + 2

Explanation:

The form of the equation that passes through two points (x1, y1) and (x2, y2) is y = m x + b, where

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

• b is the y-intercept, you can find it by substituting x, y in the equation by (x1, y1) OR (x2, y2)

Let us solve the question:

∵ The line passes through the points (-3, -2) and (3, 6)

∴ x1 = -3 and x2 = 3

∴ y1 = -2 and y2 = 6

→ Use the rule of m to find it

∵
`m=(6-(-2))/(3-(-3))=(6+2)/(3+3)=(8)/(6)`

→ Simplify it by dividing up and down by 2

∴ m =
`(4)/(3)`

→ Substitute its value in the form of the equation above

∴ y =
`(4)/(3)` x + b

→ To find b substitute x and y by x1 and y1

∴ -2 =
`(4)/(3)` (-3) + b

∴ -2 = -4 + b

→ Add 4 to both sides

∴ -2 + 4 = -4 + 4 + b

∴ 2 = b

→ Substitute it in the form of the equation

∴ y =
`(4)/(3)` x + 2

∴ The equation of the line is y =
`(4)/(3)` x + 2