DSAT - Algebra

General form of Linear Equations in One Variable

ax + b = c

Solve for x : Linear Equations in One Variable

x = \frac{c-b}{a}

slope intercept form

y = mx + b

Slope point form

y-y1=m\left(x-x_1\right)

Two variable Linear equations: Standard form

Ax + By = C

Two variable Linear equations: x intercept

set y to 0 then Ax = C

Two variable Linear equations: y intercept

x to 0 then solve By = C

Two variable Linear equations: how to get slope

m = -\tfrac{A}{B}

Systems of Linear Equations: graphing

use desmos

Systems of Linear Equations: substitution

Solve one equation for x or y then substitute into the other

Systems of Linear Equations: elimination

multiply equations (if needed) so coefficients align; add/subtract to eliminate one variable.

Linear Inequalities: solving

same as equations but flip inequality when multiplying/Diving by a negative

Function Transformations: Horizontal shift

f(x) \to f(x-h) → shift right by h if h>0 (remember “minus means right”).

Function Transformations: Vertical shift

f(x) \to f(x)+k → shift up by k if k>0

Function Transformations: Vertical Reflection

(a,-b)

Function Transformations: Horizontal Reflection

(-a, b)

Function Transformations: Origin Reflection

(-a, -b)

Function Transformations: across y=x Reflection

(b,a)

Function Transformations: Rotation 90 degrees counter clockwise

(x, y) becomes (-y, x)

Function Transformations: Rotation 180

(x, y) becomes (-x, -y)

Function Transformations: Rotation 270 counterclockwise

(x, y) becomes (y, -x)

Function Transformations: Dilation

Image = (Pre-Image_ *|scale factor|