Linear Equations

I can recognize a linear relationship from a table, graph, and/or equation

Why-

A relationship between two quantities in which one variable changes at a constant amount as the other variable changes by a constant amount.

Linear Relationship

Positive Linear Relationship- The line increases(rises) from left to right.y=mx+b

Negative Linear Relationship- The line decreases(falls) from left to right.y=-mx+b

Zero Linear Relationship- The line neither increases or decreases from left to right.y=(any number)

A constant ratio of two variables related proportionally

Constant of proportionality

x

yk

X (variable) Y(total)

1 2

21

2

k

kkxy

A mathematical sentence that shows that two

expressions are equivalent.

Equation

110510 x

110 xy

11065

A linear equation written in the form y=mx+b, where m

represents the slope and b represents the y-intercept

Slope

Y-intercept

Slope-Intercept equation

bmxy

32 xy

Slope

y-intercept

A measure of the steepness of a line on a graph; the rise divided by the run.

m=== change in or difference

SlopeX Y

1 2

2 3

11

1

12

23

mSlope

X-Axis: it’s the axis that runs horizontal, where point (x,y)

y=0, on the coordinate plane. The x-axis runs from left to right.

Y-Axis: it’s the axis that runs vertical, where point (x,y) x=0, on the coordinate plane. The y-axis runs from top to bottom.

X-Axis

Y-Axis

x-axis

y-axis

Origin(0,0)

Origin(0,0)

The point where the graph of a line passes the y-axis. In

equation y=mx+b, the y-intercept equals the b value (0,b).

Y-intercept = (0,3)

Y-intercept

Y-Intercept

32 xy

X Y

-1 1

0 3

1 5

y-intercept

Quadrant II

(-,+)

Quadrant I

(+,+)

Quadrant III

(-,-)

Quadrant IV

(+,-)

Coordinate Plane (graph)

Liner Relationshippositive-negative-zero

d) e) f)

a) b) c)

Label the following points and quadrant.

d) e) f)

a) b) c)

Quadrant II(-,+)