Question

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Answer 1

The equation of the line is y =
`-(4)/(5)` x +
`(3)/(5)`

Explanation:

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

• m is the slope

• b is the y-intercept

The rule of the slope is m =
`(y2-y1)/(x2-x1)` , where

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

∵ A line passes through points (2, -1) and (-3, 3)

∴ x1 = 2 ad y1 = -1

∴ x2 = -3 and y2 = 3

→ Use the rule of the slope above to find the slope of the line

∵ m =
`(3--1)/(-3-2)` =
`(3+1)/(-5)` =
`(4)/(-5)`

∴ m =
`-(4)/(5)`

→ Substitute the value of m in the form of the equation above

∴ y =
`-(4)/(5)` x + b

→ To find b substitute x and y in the equation by the coordinates of one

point of the given points

∵ x = 2 and y = -1

∴ -1 =
`-(4)/(5)` (2) + b

∴ -1 =
`-(8)/(5)` + b

→ Add
`(8)/(5)` t both sides

∵ -1 +
`(8)/(5)` = b

∴
`(3)/(5)` = b

→ Substitute the value of b in the equation

∴ y =
`-(4)/(5)` x +
`(3)/(5)`

∴ The equation of the line is y =
`-(4)/(5)` x +
`(3)/(5)`