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Write the equation of a line in standard form

Slope equal to 2 and passing through (-5,1)

Ralph L. | Algebra I, II, Visual Basic, Beginning C++ tutorAlgebra I, II, Visual Basic, Beginning C...
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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
Chris I. | Microbiology Degree and Years of Experience in Computer ScienceMicrobiology Degree and Years of Experie...
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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

2X - Y = -11

A = 2
B = -1
C = -11

The check:
-11 = 2 (-5) - (1) = -11
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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

Ensure coefficient of x is positive by multiplying the equation by -1(both sides, all terms)

2x - y = -11