Math-Chapter 3

X-intercept

The X coordinate of the point where the graph crosses the x-axis. Since any linear equation can be graphed using two points, you can use the x and y intercepts to graph an equation.

Constant Rate of Change

The rate of change between any two points in a linear relationship is the same or constant. A linear relationship has a constant rate of change.

Y-intercept

The y intercept of a line is the y-coordinate of the point where the line crosses the y-axis. (In a non proportional linear relationship, the graph passes through the point (0,b) or the y-intercept). Y=mx + b (*b represents the y intercept)

Rise

Veritical Change between any two points

Direct Variation:

When the ratio of Two variable quantities is constant, a proportional relationship exists. This relationship is called a direct variation. Y=Mx. Where m is the constant of variation and m does not equal 0.

The Constant ratio

is called the Constant of Variation or Constant of Proportionality.

SLOPE FORMULA

m= y2- y1/x2 - x1 where x2 DOES NOT Equal X1 **It does not matter which points you define as (x1,y1) and (x2,y2). You must use points in same order

*Important Reminders Of Slopes and Intercepts when a linear system of equations has: ——> Different slopes and y-intercepts,

there is one and only one solution.

Systems of Equations

A set of Two or more equations that contain two or more variable. (Example: y=4x and y=4x + 2 together are a system of equations).

Substituion

Algebraic model that can be used to find the exact solution of a system of equations. Substitution is when you replace a variable with an expression,write the expression inside the parenthesis. This will help you apply the Distributive Property correctly.

Standard Form

Ax + By = C

Run

Horizontal Change between any two points

Solution to a System of Equations

Solution to a System of Equations is a set of values that make all equations in a system true.

The same slope and same y intercept

The Same slope and same y-intercepts,there is an infinite number of solutions.

Linear Relationship

Relationships that have straight-line graphs

Slope

Slope is a rate of change. It can be positive (slanting upwards) or negative (slanting downward). Slope=RISE/RUN In linear relationships, no matter which two points you chose,the slope, or rate of change of the line is always constant.

Proportional Relationships

two quantities a and b have a proportional linear relationship if they have a constant ratio and a constant rate of change; b/a is constant and change in b/change in a is constant. *To determine if two quantities are proportional, compare the ratio b/a for several pairs of points to determine if there is a constant ratio

Point-slope form

y - y1= m (x - x1) is written in point-slope form, where (x1, y1) is a given point on a non vertical line and m is the slope of the line. ***You can write an equation of a line in slope-intercept form when you know the slope and the y intercept. You can write an equation in a point-slope form when you are given the slope and the coordinates of a point on the line that is not the y-intercept.

Slope-intercept form:

y=mx + b is the Slope Intercept Form (m=slope; b is the y intercept) **In real world situation, the slope represents the rate of change and the y intercept represents the initial value.

The same slope and different y intercepts

—> The Same slope and different y-intercepts, there is NO solution