Systems of Linear Equations. Forms and Solutions.

Could you graph a linear equation if they gave you a point and the slope? What about if you are given the slope and the y-intercept? How is this related to the solution of systems of linear equations by graphing?

Do you know how to solve systems of linear equations by substitution and elimination? What is a Greatest Integer Function, or a Constant Function?

Try to go through this lesson and find the answers for all these questions. Very recommended is that you take the time to review the vocabulary given below the box where the lesson is displayed scrolling down the screen. A section with some animated gifs highlights important concepts in a visual graphic way. While going throughout the lesson you might need to highlight sections or write notes and come back to them using the thumbnails at the left. This is accomplished using the MARKER TOOLS menu on the upper right top of the screen. You are going to be guided in a step by step process, with color clues, and minimizing long explanations in favor of visual representations of the solutions and concepts. Surely that you will like it!

Lesson's Content

Lesson In PDF Format (no animations)

PURCHASE INFORMATION

Lesson's Glossary

Equivalent system:  A system of equations having the same solution set as another system.

Graph of an equation in two variables:  All the points that may be graph from the solution set of the equation.

Graph of a function:  The solution set graphed for the function in the given domain.

Graph of a number:   The location of a point paired with a number in the number line.

Graph of an ordered pair:  The location in the coordinate plane associated with an ordered pair of real numbers.

Linear equation:   Any equation with all exponents = 1 regardless of the form the equation is represented.

Linear equation in two variables:   All equivalent equations to the one in the form of ax + by = c, where a, b, and c are in the set of the real numbers and a and b can't be zero at the same time. The graph is a straight line.

Linear function:  A function of the form: f(x) = mx + b.

Ordered pair:   In a coordinate plane is the location of a point.

Ordinate:  The y-coordinate in an ordered pair of the coordinate plane.

Origin:   The location of the zero point in a number line.

Parallel lines:   Lines with the same slope. Lines in the same plane that don't intersect.

Perpendicular lines:   Lines that intersect or cross at right angles. Multiplying the slopes of perpendicular lines always yield -1.

Plot a point:   Locating and graphing an ordered pair of real numbers in the coordinate plane.

Point-slope form of an equation:  Y - Y1 = m(X-X1), where m is the slope and (X1 , Y1) the point for which the line goes through.

Slope of a line: The measure of how steep a line is. The change in y (rise) divided by the change in x (run). Slope = m

Slope-intercept form of an equation:   The equation of a line in the form y = mx + b, where m represents the slope, and be represents the y-intercept.

Solution of an equation in two variables:  Any ordered pair of real numbers that makes the sentence true.

Solution of a system of two equations in two variables:   Ordered pair that when replaced in the equations produces a true statement for both equations.

Solve a system of two equations in x and y:   Finding all ordered pairs (x,y) which make both equations in the system true.

Standard form of a linear equation:   ax + by = c, where a, b, and c are integers and a and b are not both zero.

x-intercept:  The x-coordinate of a given point for which the graph intersects the x-axis.

y-intercept: The y-coordinate of a given point for which the graph intersects the y-axis.

Vocabulary Highlights

Slope of a line: The measure of how steep a line is. The change in y (rise) divided by the change in x (run). Slope = m

Slope of a Line

Slope-intercept form of an equation:   The equation of a line in the form y = mx + b, where m represents the slope, and be represents the y-intercept.

Slope Intercept

Point-slope form of an equation:  Y - Y1 = m(X-X1), where m is the slope and (X1 , Y1) the point for which the line goes through.

Point Slope Form

Slope-intercept form of an equation:  

The equation of a line in the form y = mx + b,

where m represents the slope, and be represents the y-intercept.

 

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