Question

Find the slope of the line satisfying the given conditions

a) through (-3,4) and (2,-8)

b) through (5,-3) and (1,-7)​

Answer 1

a) The slope of the line is
`-(12)/(5)`

b) The slope of the line is 1

Explanation:

The rule of the slope of a line that passes through points (x1, y1) and (x2, y2) is m =
`(y2-y1)/(x2-x1)`

a)

∵ The line passes through points (-3, 4) and (2, -8)

∴ x1 = -3 and y1 = 4

∴ x2 = 2 and y2 = -8

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

∵ m =
`(-8-4)/(2--3)` =
`(-12)/(2+3)` =
`(-12)/(5)`

∴ m =
`-(12)/(5)`

∴ The slope of the line is
`-(12)/(5)`

b)

∵ The line passes through points (5, -3) and (1, -7)

∴ x1 = 5 and y1 = -3

∴ x2 = 1 and y2 = -7

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

∵ m =
`(-7--3)/(1-5)` =
`(-7+3)/(-4)` =
`(-4)/(-4)`

∴ m = 1

∴ The slope of the line is 1