Question

Choose the equation that represents a line that passes through points (-1, 2) and (3, 1).

Answer 1

Answer:

B. x + 4y = 7

Step-by-step explanation:

$\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\==============================$

$\text{We have the points (-1, 2) and (3, 1). Substitute:}\\\\m=\dfrac{1-2}{3-(-1)}=\dfrac{-1}{4}=-\dfrac{1}{4}\\\\\text{Put the value of a slope and the coordinates of the point (3, 1) }\\\text{to the equation of a line:}\\\\y-1=-\dfrac{1}{4}(x-3)\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y-1=-\dfrac{1}{4}(x-3)\qquad\text{multiply both sides by 4}\\\\4y-4=-(x-3)\\\\4y-4=-x-(-3)\qquad\text{add x to both sides}\\\\x+4y-4=3\qquad\text{add 4 to both sides}\\\\x+4y=7$