Linear Relationships: Equations

Solving linear equations form a basis for all the solving techniques that are used to solve algebraic equations.

Slope Intercept Form of an Equation


Here is the slope-intercept form of an equation:

Parts of a Linear Equation

slope equation

Y = a total

m= slope = rate (per, each)

X = number of something

B = y-intercept, the starting point (fee)

 

Slope and Y Intercept


A slope is a number that describes the direction and steepness of a line graph. It is expressed as a ratio or rate.

The Y-intercept is the point where a graph on the coordinate plane intersects the y-axis. It the starting value before the situation is affected by a rate.

Steps for Solving an Equation


The goal when solving any equation is to **Isolate the variable** This is done by following the steps that follow:

 

  1. Distributive Property- remove the parenthesis from the equation
  2. Combine Like Terms – simplify the equation
  3. Inverse operations (add and subtract integers)- get all the rational numbers on one side of the equal sign.
  4. Inverse operations (multiply and divide coefficients)- finalize finding the solution to the variable by separating the coefficients

Special Linear Equations


Some linear equations serve special purposes

Infinitely Many solutions (all solutions for X is true) – Any value for X makes the equation true.

No solutions – There is no value of X that makes the equation true.

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More on Solving Equations

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