Section 8.2 Equations with Two Variables pages

In today’s lesson, we will find solutions of equations with two variables, such as y = 3x + 4. An _______ ____ that makes such an equation a true statement is a ________ of the equation.

Example 1: Finding a Solution Find the solution of y = 3x + 4 for x = -1. y = 3x + 4 y = 3(-1) + 4 y = y = 1 So, a solution of the equation is (-1,1) Replace x with -1. Multiply. Add.

Why does the last line of the example say, “A solution of the equation…” instead of “The solution of the equation…?”

Example 2 The equation t = n models the normal low July temperature in degrees Celsius at Mount Rushmore, South Dakota. In the equation, t is the temperature at n meters above the base of the mountain. Find the normal low July temperature at 700m above the base.

Graphing Equations with Two Variables An equation with two variables can have many solutions. One way to show these solutions is to graph them, which also gives the graph of the equation. A ______ ________ is any equation whose graph is a line. The coordinates of every point on a line in a coordinate plane make the equation of the line a true statement.

Graphing a Linear Equation Graph y = 4x – 2. Make a table of values to show ordered pair solutions. xy = 4x – 2(x,y)

Graph the ordered pairs. Draw a line through the points. y x y (-2,-10) (0,-2) (2,6)

If you use the vertical-line test on the previous graph, you see that every x-value has exactly one y- value. This means that the relation y = 4x – 2 is a ________. A linear equation is a ________ unless its graph is a vertical line.

Graphing a Linear Equation Graph y = 2x + 1. Make a table of values to show ordered pair solutions. xy = 2x + 1(x,y)

Graph the ordered pairs. Draw a line through the points. y x y (-2,-3) (0,1) (2,5)

Graphing a Linear Equation Graph y = 1 / 2 x + 4. Make a table of values to show ordered pair solutions. x y = 1 / 2 x + 4 (x,y)

Graph the ordered pairs. Draw a line through the points. y x y (-2,3) (0,4) (2,5)