EdReady: Coordinate Plane

Coordinate Plane, Graphing Linear Equations, Finding the Slope of a Line, Writing the Equation of a Line, Parallel and Perpendicular Lines, Graphing Linear Inequalities

Quadrant pattern

I: (+, +)

II: (-, +)

III: (-, -)

IV: (+, 0

the dependent value is always

y

linear relationship

relationship that can be represented as a line

linear equation

equation with a degree of one

intercepts

where the line meets an axis

x-intercept

when y = 0

y-intercept

when x = 0

x value is

vertical line

y value is

horizontal line

How to see if an ordered pair is the solution of a linear equation

Graph the linear equation and ordered pair

Substitute the x, y values into the equation

slope

measures steepness of line

slope =

rise/run

rise

vertical movement

run

horizontal movement

A steeper line means…

larger slope

Downhill line

rise is negative

Uphill line

rise is positive

Run moves left to right when

positive

Run moves right to left when

negative

slope formula

m = rise/run = y2 - y1/x2 - x1

when rise = 0

horizontal line, slope = 0, 0/x

when run = 0

vertical line, slope = undefined, x/0

full slope formulations

m = rise/run = Δy/Δx = y2 - y1/x2 - x1

Δ

change

slope-intercept form

y = mx + b; m = slope, b = y-intercept

If slope, one point, no intercept

substitute (x and y) and solve for b, use slope and b to write the formula

If two points

find slope, substitute values and for b, use slope and b to write formula

m = 0

horizontal line

if m is positive

line slopes up (from left to right)

if m is negative

line slopes down (from left to right)

y-intercept changes

moves line up and down

positive y-intercept

line crosses y-axis above origin

negative y-intercept

line crosses y-axis below origin

parallel lines in slope-intercept form

lines with same slope and different y-intercepts

perpendicular lines

meets at right angles

perpendicular lines in slope-intercept form

opposite and reciprocal slopes (slope = -1/m)

When m = 0

line form y=a is a constant

When finding parallel/perpendicular lines with two points

set problem to slope intercept form

ID slope and create new equation in slope-intercept form

substitute x and y values and solve for b

How to graph linear inequalities

place inequality into slope-intercept form

create boundary line: replace inequality sign with equals sign

graph boundary line with a dashed or solid line

plot and test example points on both sides of line

shade side with points that make inequality true

When to shade above or below the boundary line

shade below if y less than (or equal to) x

shade above if y greater than (or equal to) x

dashed line

less than or greater than; boundary is not included in solution

solid line

less/greater than or equal to; boundary is included in solution