Transcript Standard Form Ax + By = C

Standard
Form
TOOLBOX:
SUMMARY:
Standard Form
Ax + By = C
Slope: Rise
Run
Slope Formula: y2 – y1
x2 – x1
Write the equation in standard form with
integer coefficients.
1)
y = 7x – 9
-7x
Original Problem
Get into standard form Ax + By = C
Inverse of 7x is -7x
-7x
-7x + y = -9
*Read Directions
Solution
2)
5y = ¾x + 2
Original Problem
Integers: NO FRACTIONS!
(4)5y = (4)¾x + (4)2
20y = 3x + 8
-3x
-3x
-3x + 20y = 8
3)
Get rid of 4 on bottom
by multiplying everything by 4
Get into standard form: Ax + By = C
Inverse of 3x is -3x
Solution
-3y = - ½x – 15
Original Problem
Integers: NO FRACTIONS!
-3y(2) = - ½x(2) – 15(2)
Get rid of 2 on bottom
by multiplying everything by 2
-6y = -1x + 30
+1x +1x
x – 6y = –30
Solution
Get into standard form: Ax + By = C
Inverse of -x is +x
Write in standard form the
equation of the line that passes
through the given point and has
the given slope.
4) (-3,7) with slope -2
y – y1 = m(x – x1)
*Read Directions
Original Problem
Use point-slope form first
Sub -3 for x1, 7 for y1, and -2 for m
y – 7 = -2(x + 3)
Now get into Standard Form
Ax + By = C
Inverse of -7 is +7
y – 7 = -2x – 6
+ 7
+ 7
y = -2x + 1
+2x +2x
2x + y = 1
Inverse of -2x is +2x
Solution