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Write the equation of a line in standard form

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3 Answers

slope intercept form of equation for line:
 
y = mx + b
given:
 
m = 2, x = -5, y = 1
 
1 = 2(-5) + b
 
1 = -10 + b
 
b = 11
 
so equation:
 
y = 2x + 11  equation(1)
 
standard form for equation of line is:
 
Ax + By = C, so we rearrange the equation (1)
 
 
2x  - y = -11
Standard Form of a line is:
Ax + By = C where A is a positive integer, and B, and C are integers.
 
So we have a few conditions we must meet.
 
We can plug those numbers into our slope-intercept equation (Y= M * X + B) where M is the slope and B is the Y-intercept.
 
We will first use the points to solve for B, and then convert that to Standard Form:
 
Solve for B:
 
1 = 2 * (-5) + B
1 - ( 2 * (-5) ) = B
1 + 10 = B = 11
 
Convert to Standard Form:
Y = 2 * X + 11 ; Subtract Y from both sides to keep A positive
0 = 2 * X - Y + 11; Subtract 11 from both sides
-11 = 2X - Y
 
Answer
2X - Y = -11
 
A = 2
B = -1
C = -11
 
The check:
-11 = 2 (-5) - (1) = -11
The standard equation of a line with a slope m and an intercept b is given by the equation
 
y= mx + b
 
However when given only the slope and a point of interception not on the y-axis, we best use the slope intercept formula which is given by;
 
(y-y1)=m(x-x1)
 
where (x1,y1) is the point of intersection and m is the slope. We will substitute and solve for y.
 
y-1 = 2(x-(-5))
y-1 = 2x+10
y = 2x+ 11
 
Therefore the standard form for the equation in question is
y-2x=11