Answer:
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 − m x
y − m x
=(mx−mx)+b
=b
\begin{aligned} y - mx - b &= b - b \\ y - mx - b &= 0 \end{aligned}
y − m x − b
y − m x − 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
3 x+
10
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