Use a determinant to find an equation of the line passing through the points (-5,-1)and (2,4).
A)5x + 7y - 18 = 0
B)-5x - 7y - 18 = 0
C)-5x + 7y + 18 = 0
D)5x - 7y - 18 = 0
E)-5x + 7y - 18 = 0

Question

Use a determinant to find an equation of the line passing through the points (-5,-1)and (2,4). ​
A)5x + 7y - 18 = 0
B)-5x - 7y - 18 = 0
C)-5x + 7y + 18 = 0
D)5x - 7y - 18 = 0
E)-5x + 7y - 18 = 0

Quizplus · Accepted Answer

We can use the determinant method to find the equation of the line passing through two points. The determinant gives us the coefficients of the equation in the form of Ax + By + C = 0.

|x1  y1  1|
|x2  y2  1|
 
Plugging in the values we get,

|-5  -1  1|
|2   4   1|

= (-5)(4) - (-1)(2)
= -20 + 2
= -18

So, the equation of the line is

-5x + 7y - 18 = 0.

Therefore, the best choice is E.

Use a Determinant to Find an Equation of the Line