Find the standard form equation of the line that passes through the points (2,-10) and (7,-9).
Answer (2)
To find the standard form equation of a line through the points (2, -10) and (7, -9), we first calculate the slope which is 5 1 . Then, using the point-slope form, we rearranged it to get the standard form equation: x − 5 y = 52 .
;
To find the standard form of the equation of the line passing through the points ( 2 , − 10 ) and ( 7 , − 9 ) , we can follow these steps:
Find the slope (m):
The slope of a line through two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is calculated as: m = x 2 − x 1 y 2 − y 1 Using the given points ( 2 , − 10 ) and ( 7 , − 9 ) : m = 7 − 2 − 9 − ( − 10 ) = 5 1
Use the point-slope form of the equation:
The point-slope form of a line's equation is: y − y 1 = m ( x − x 1 ) Substituting one of the points, say ( 2 , − 10 ) , and the slope we found: y + 10 = 5 1 ( x − 2 )
Convert the equation to standard form:
The standard form of a line's equation is: A x + B y = C First, distribute the slope on the right side: y + 10 = 5 1 x − 5 2 Multiply through by 5 to eliminate the fraction: 5 ( y + 10 ) = x − 2 Simplify: 5 y + 50 = x − 2 Rearrange the terms to get it into standard form: x − 5 y = 52
Thus, the standard form equation of the line passing through ( 2 , − 10 ) and ( 7 , − 9 ) is: x − 5 y = 52
