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Questions and Answers
What is the algebraic representation of the equation 3x + y = 7?
What is the algebraic representation of the equation 3x + y = 7?
- y = -3x + 7 (correct)
- y = 3x + 7
- x = 3y - 7
- x = -3y + 7
What is the purpose of constructing a table of values in graphing an equation?
What is the purpose of constructing a table of values in graphing an equation?
- To find the equation of the graph
- To identify the x-intercept of the graph
- To recognize patterns and identify solution points of the equation (correct)
- To determine the slope of the graph
What is the graphical representation of the equation y = -3x + 7?
What is the graphical representation of the equation y = -3x + 7?
- A circle
- A hyperbola
- A line (correct)
- A parabola
What is the x-coordinate of the y-intercept of the graph of y = -3x + 7?
What is the x-coordinate of the y-intercept of the graph of y = -3x + 7?
How many solution points are required to graph a linear equation?
How many solution points are required to graph a linear equation?
What is the value of y when x = -2 in the equation y = -3x + 7?
What is the value of y when x = -2 in the equation y = -3x + 7?
What is the relationship between the variables x and y in the equation y = -3x + 7?
What is the relationship between the variables x and y in the equation y = -3x + 7?
What is the purpose of rewriting the equation 3x + y = 7 in the form y = -3x + 7?
What is the purpose of rewriting the equation 3x + y = 7 in the form y = -3x + 7?
What is the value of x when y = 4 in the equation y = -3x + 7?
What is the value of x when y = 4 in the equation y = -3x + 7?
What is the graphical representation of the solution points (-2, 13), (-1, 10), (0, 7), (1, 4), (2, 1), and (3, -2)?
What is the graphical representation of the solution points (-2, 13), (-1, 10), (0, 7), (1, 4), (2, 1), and (3, -2)?
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Study Notes
Graphs of Equations
- A graph of an equation can help visualize relationships between real-life quantities.
- An equation in two variables, such as y = 7 − 3x, represents a relationship between two quantities.
- An ordered pair (a, b) is a solution or solution point of an equation in x and y when the substitutions x = a and y = b result in a true statement.
Solution Points
- To determine whether a point (a, b) lies on the graph of an equation, substitute x = a and y = b into the equation.
- If the substitution results in a true statement, then the point (a, b) is a solution point of the equation.
Sketching Graphs of Equations
- To sketch the graph of an equation, rewrite the equation to isolate y on the left.
- Construct a table of values with several solution points of the equation.
- Plot the solution points and complete the sketch by drawing a line or curve through the points.
X- and Y-Intercepts
- The x-intercept is the point where the graph intersects the x-axis.
- The y-intercept is the point where the graph intersects the y-axis.
Symmetry in Graphs
- Symmetry can be used to graph an equation.
Equation of a Circle
- The standard form of the equation of a circle is given on page 17.
Real-Life Applications
- Graphs of equations can be used to solve real-life problems, such as analyzing life expectancy.
- Example 9 on page 18 shows how to use the graph of an equation to solve a real-life problem.
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