Math 1.6 Linear Equations in Two Variables

Finding intercepts

Finding intercepts * To find the x-intercept(s), if any, of the graph of an equation, let y = 0 in the equation and solve for x. (when y = 0, you find the x-intercept(s). * To find the y-intercept(s), if any, of the graph of an equation, let x = 0 in the equation and solve for y. (when x = 0, you find the y-intercept(s).

In Words: define slope

In Words: Slope is the change in y divided by the change in x.

Definition m=(y#2-y#1) / (x#2-x#1), x#1 ≠ x#2, m = rise / run m represents the slope

Let P = (x#1, y#1) and Q + (x#2, y#2) be two distinct points. If x#1 ≠ x#2, the *slope* m of the nonvertical line L contains P and Q is defined by the formula: m=(y#2-y#1) / (x#2-x#1), x#1 ≠ x#2, If x#1 = x#2, then L is a vertical line and the slope m of L is *undefined* (since this results in division by 0)

Standard form for a linear equation

Standard for for a linear equation is: Ax + By = C

Slope of a line given two points

We call the ratio of the rise to the run (rise over run) the slope of the line.

Work Smart Linear equations

Work Smart: Linear equations in one variable have no solution, one solution, or infinitely many solutions. Because the procedure for finding intercepts of linear equations in two variable results in a linear equation in one variable, linear equations can have no x-intercepts, on x-intercept, or infinitely many x-intercepts. The same applies to y-intercepts.

Work Smart Find 3 points show interesting features such as its intercepts

Work Smart: We recommend that you find at least three points when graphing linear equations to be sure your graph is correct. Also, remember that a complete graph is a graph that shows all the interesting features of the graph, such as its intercepts.

Graphing Linear Equations Using the Point-Plot Methods Work Smart

You can choose to pick x-values and use the equation to find the corresponding y-values; however, we could also choose the y-values and used the equation to find the corresponding x-values. Either way works.

Graphing a Horizontal line: Equation of a Horizontal Line Example: y = -2

A *horizontal line* is given by an equation of the form: y = b where (0,b) is the y-intercept.

Definition: Linear equation in two variables

A *linear equation in two variables* is an equation of the form: Ax + By = C where A, B, and C are real numbers. A and B cannot be 0.

Graphing a Vertical Line: Equation of a Vertical Line Example: x = 3

A *vertical line* is given by an equation of the form: x = a where (a,0) is the x-intercept.