Question

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

A. 4x - y = -6
B. x + 4y = 7
C. x - 4y = -9
D. 4x + y = 2

Answer 1

B. x + 4y = 7

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=(y_2-y_1)/(x_2-x_1)\\\\==============================`

`\text{We have the points (-1, 2) and (3, 1). Substitute:}\\\\m=(1-2)/(3-(-1))=(-1)/(4)=-(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=-(1)/(4)(x-3)\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y-1=-(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`