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

Answer:  Equation of line = $y=-4x+9$

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

Step-by-step explanation:

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

$m=\dfrac{d-b}{c-a}$

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

$m=\dfrac{5-(-7)}{1-4}\\\\\Rightarrow\ m=\dfrac{5+7}{-3}\\\\\Rightarrow\ m=\dfrac{12}{-3}\\\\\Rightarrow\ m=-4$

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.

Answer 2

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