Question

Write the equation of the line that contains the points (4, −7) and (1, 5). The slope of the line that contains the points (4, −7) and (1, 5) is .

Answer 1

slope = (5+7)/(1-4) = 12/-3 = -4

slope = -4

y = mx + b
-7 = -4(4) + b
-7 = -16 + b
b = 9

equation
y = -4x + 9

Answer 2

Answer: Equation of line =
`y=-4x+9`

The slope of the line that contains the points (4, −7) and (1, 5) is -4 .

Explanation:

The slope of a line that contains two points (a,b) and (c,d) is given by :-

`m=(d-b)/(c-a)`

The slope of a line passing through (4, −7) and (1, 5) will be:_

`m=(5-(-7))/(1-4)\\\\\Rightarrow\ m=(5+7)/(-3)\\\\\Rightarrow\ m=(12)/(-3)\\\\\Rightarrow\ m=-4`

The equation of a line passing through (a,b) and has slope m is given by :_

`(y-b)=m(x-a)`

Then , the equation passing through (1,5) and has slope -4 will be

`(y-5)=-4(x-1)\\\\\Rightarrow\ y-5=-4x+4\\\\\Rightarrow\ y=-4x+4+5\\\\\Rightarrow\ y=-4x+9`

Hence, the equation of line =
`y=-4x+9`

The slope of the line that contains the points (4, −7) and (1, 5) is -4.