How to convert a slope intercept equation to standard form

To convert from slope intercept form y = mx + b to standard form Ax + By + C = 0, let m = A/B, collect all terms on the left side of the equation and multiply by the denominator B to get rid of the fraction.

Step-by-step explanation:

y = mx + b

y=mx+b

\begin{aligned} y - mx &= (mx - mx ) + b \\ y - mx &= b \end{aligned}

y−mx

y−mx

=(mx−mx)+b

=b

\begin{aligned} y - mx - b &= b - b \\ y - mx - b &= 0 \end{aligned}

y−mx−b

y−mx−b

=b−b

=0

-mx + y - b = 0

−mx+y−b=0

Example:

(1) - The equation of a line in slope intercept form is:

y = \frac{1}{2} x + 5

y=2

1x+5

What is the equation in standard form?

y - \frac{1}{2}x = 5

y−2

1x=5

y - \frac{1}{2}x - 5 = 0

y−2

1x−5=0

2y - x - 10 = 0

2y−x−10=0

-x + 2y - 10 = 0

−x+2y−10=0

You can leave the equation like this, but if you prefer to make x positive, multiply both sides by -1:

x - 2y + 10 = 0

x−2y+10=0

or

x - 2y = -10

x−2y=−10

(2) - The slope of a line is -3/7 and the y-intercept is 10. What is the equation of the line in standard form?

The slope intercept form of the line is

y = -\frac{3}{7}x + 10

y=

−7

3x+

10

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