1.9 Coordinate Plane - 1.12 Modeling Variation

Distance formula

Midpoint formula

X-intercepts

Set y=0 and solve for x

Y-intercepts

Set x=0 and solve for y

Circle

Symmetry with respect to the x-axis

Replace y with -y and the resulting equation is equation is equivalent to the original one

Symmetry with respect to the y-axis

Replace x with -x and the resulting equation is equivalent to the original one

Symmetry with respect to the origin

Replace x with -x and y with -y and the resulting equation is equivalent to the original

Slope

Rise over run

Point slope form

Slope-intercept form

Vertical line

x=a

Horizontal line

y=a

General form

Ax + By + C = 0

Parallel lines

Two non vertical lines that have the same slope

Perpendicular lines

Two lines with a slopes that are opposite reciprocals

Direct variation

y=ky

Inverse variation

y=k/x