Given two points on the line, input the equation of the line in standard form Ax + By = C. Reduce all fractional answers to lowest terms.

(-8, 0), (1, 5)

Question

Given two points on the line, input the equation of the line in standard form Ax + By = C. Reduce all fractional answers to lowest terms.

(-8, 0), (1, 5)

anonymous · Answer

Before we input the equation of the line, since 2 points in the line are given, we can solve for the slope of the line...$$m=\frac{ (5-0) }{ (1-(-8)) }=\frac{ 5 }{ 9 }$$

anonymous · Answer

and from definition of slope of a line, other points satisfy the equation of a line considering a given point, either (-8,0) or (1,5)... other points (x,y)....$$m = \frac{ (y-y _{1}) }{ (x-x _{1}) }$$

anonymous · Answer

choosing (1,5) as the point and the slope m=5/9... we have...$$\frac{ 5 }{ 9 }=\frac{ (y-5) }{ (x-1) }$$

anonymous · Answer

5(x-1) = 9(y-5) ... by cross multiplication
5x-5 = 9y-45   ... by distributive property
5x - 9y - 5 + 45 = 0  ... by transposistion

5x - 9y + 40 = 0  ... the equation of the line

anonymous · Answer

to check, we can substitute the other point (-8,0)...

5 (-8) - 9 (0) + 40 = 0