Write each English sentence as an equation in two variables. Then graph the equation. The y -val

Write each English sentence as an equation in two variables....

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Key Concepts

Translating English Statements to Algebraic Equations

This concept involves reading a verbal description of a relationship and expressing it mathematically using variables and operations. It requires identifying key phrases that indicate mathematical operations (such as 'difference', 'twice', etc.) and forming an equation that accurately represents the given statement.

Linear Equations in Two Variables

A linear equation in two variables is an algebraic equation that can be expressed in the form Ax + By = C, where A, B, and C are constants. These equations graph as straight lines on the coordinate plane and describe a constant rate of change between the variables.

Graphing Equations

Graphing equations involves plotting the relationship defined by an equation on a coordinate plane. For linear equations, this typically includes finding intercepts or using the slope-intercept form, then drawing a straight line that represents all solutions to the equation.

Understanding Variables

Variables are symbols that represent unknown quantities in mathematics. They allow for generalization and manipulation of equations. In the context of graphing, variables determine the coordinates on the picture plane, facilitating the visualization of relationships between quantities.

Transcript

00:01 I need to translate this verbal sentence into an algebraic equation, and then we'll fill in a table of values for ordered pairs so we can graph the equation.

00:13 To begin with, the phrase the y value is represents your y variable and the word is means equal to.

00:23 The difference means we are going to subtract, and then the order that the information is given to you is the order we're going to subtract it.

00:35 So between 4 and twice the x value, so that's 4 and twice the x value.

00:44 So that is the equation y equals 4 minus 2x is the equation for the y value is the difference between 4 and twice the x value.

00:57 So now let's create a table of values.

01:00 Let's use negative 2, negative 1, 0, 1, 2, and 3.

01:09 So we've got y equals 4 minus 2 times our input x value of negative 2.

01:16 So that's why negative 2 times negative 2 is 4, so that's 4 plus 4 is 8.

01:28 Next we have 4 minus 2 times negative 1.

01:32 Negative 2 times negative 1 is positive 2, so that's 4 plus 2 is 6.

01:44 4 minus 2 times 0.

01:47 Well, 2 times 0 is 0, so this is 4.