Linear Equations 2, Linear Equations

linear equation

An equation in two variables whose graph in a coordinate plane is a straight line.

slope

A ratio comparing the change in output over the change in input of a line. The steepness of a line.

y-intercept

The value of the output when the input is zero (0, y). The point where a graph crosses the y-axis.

x-intercept

The value of the input when the output is zero (x, 0). The point where a graph crosses the x-axis. Also called roots, zeros or solutions.

expression

A mathematical sentence without an equal sign.

equation

A mathematical sentence that contains an equal sign.

coefficient

A number multiplied by a variable in an algebraic expression or equation.

variable

A letter or symbol that represents a number.

constant

A value that does not change.

slope-intercept form

Form for a linear equation: y = mx + b

point-slope form

Form for a linear equation: y - y1 = m(x - x1 )

standard form

Form for a linear equation: Ax + By = C

Types of Slope

undefined

No solution.

Division by zero = undefined.

The slope of a vertical line is undefined.

parallel lines

In a plane, two lines that never intersect.

Parallel lines have the same slope.

perpendicular lines

Two lines that intersect to form a 90 degree angle.

The slopes of perpendicular lines are negative reciprocals.

interpolation

The estimation of an unknown value between two known numbers.

extrapolation

The estimation of an unknown value outside of two known numbers.

linear regression

The process of fitting a line to a scatter plot. (best fit line)

independent variable

The variable we can change.

dependent variable

The outcome; the variable that depends on the input we selected.

system of equations

A set of two or more equations using the same variables.

1 solution (to a system)

The point (input, output) where the equations intersect. This is the input that would yield the same output in both equations.

No solutions (to a system)

If you have two parallel lines, they will never intersect. This means that there is NO input that would yield the same output for both equations.

Infinite solutions (to a system)

If you have two equivalent lines (the same line), they will have infinite points of intersection. This means that ANY input would yield the same output for both equations.

x-intercept

the point at which the line crosses the x-axis

y-intercept

the point at which the line crosses the y-axis

(b)

slope-intercept form

the general way to write a linear equation

graph

x axis

horizontal line on a graph

y axis

vertical line on a graph

function

f(x)=ax+b

sequence

a list of numbers

arithmetic sequence

a list of number where every time you add the same number

slope/ constant rate of change

rise/run

origin

(0,0)

point-slope form

A way to write linear equations when you don't know the y-intercept.

Rise

moving from down to up

Run

moving side to side

undefined slope

ex: y = 2

zero slope

ex: x = 8

Arithmetic recursive equation

Use previous (before) term to find the next one

Line

equivalent

Different ways to write the same equation

standard form

a,b and c are integers and a is positive number

best line of fit

a line on a graph showing the general direction of points

positive slope

ex: y = 2x

negative slope

ex: y = -2x