Question

Determine the equation of the line passing through the points (-1, 1) and (1, 7).

Answer 1

Answer:

$3x + y = -4$

Step-by-step explanation:

We were given to points on the line we are trying to find, hence we are able to determine the slope/gradient.

$( - 1, \: 1) \: and \: (1, \: 7) \\ slope = \frac{ {y}^{2} - {y}^{1} }{ {x}^{2} - {x}^{1} } \\ \\ s = \frac{7 - 1}{1 - ( - 1)} \\ s = \frac{6}{2}$

Slope is equal to 3.

Since we have the value for the slope, we can now use one of the points on the line to determine the equation of the line.

note that the coefficient of x is the slope. In this case the A from the standard form (Ax + By= C) is the slope.

$\\ let \: us \: use \: the \: point \: ( - 1, \: 1) \\ a = 3 \: \: \: \: y = 1 \: \: \: x = - 1\\ ax + by = c \\ 3( - 1) + 1 = c \\ - 3 + 1 = c$

$- 2 = c \\ therefore \: the \: equation \: of \: the \\ \: line \: is \\ ax + by = c \\ 3x + y = - 4$