Determine the equation of the line that passes through 

The correct answer is: 8x - y + 18 = 0

Step by step solution:
Let the given points be denoted by

(a, b) = (-3, -6)

(c, d) = (2, 34)
The equation of a line passing through two points  and  is

Using the above points, we have

Simplifying the above equation, we have

 

Cross multiplying, we get

5(y - 34) = 40(x - 2)
Expanding the factors, we have

5y - 170 = 40 x -80
Taking all the terms in the left hand side, we have

-40x + 5y - 170 + 80 = 0
Finally, the equation of the line is

-40x + 5y - 90=0
Dividing the equation throughout by(- 5), we get
This is the required equation.
 
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We can simplify the equation in any other way and we would still reach the same equation. The general form of an equation in two variables is given by a + by + c=0, where a, b, c are real numbers. The student is advised to remember all the different forms of a line, like, slope-intercept form, axis-intercept form, etc