Graphing Linear Equations Quiz: Practice with Flashcards

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Questions and Answers

What is the general form of a linear equation in two variables, and what do the constants A, B, and C represent?

The general form of a linear equation in two variables is Ax + By = C, where A, B, and C are constants, and A and B are not both zero. The constants A and B represent the coefficients of the variables x and y, respectively, and C represents the constant term.

How is the slope of a line calculated, and what does a positive slope indicate?

The slope of a line is calculated as m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. A positive slope indicates a line that rises from left to right.

What is the purpose of the y-intercept in graphing a linear equation, and how is it found?

The y-intercept is the point where the line crosses the y-axis, and it is used as a starting point for graphing the equation. The y-intercept is found by plugging in x = 0 into the equation.

What is the difference between slope-intercept form and point-slope form of the equation of a line?

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Signup and view all the answers

What does a zero slope indicate about a line, and what is the graph of a linear equation in two variables?

A zero slope indicates a horizontal line. The graph of a linear equation in two variables is a straight line. Signup and view all the answers

What is the purpose of finding the x-intercept in graphing a linear equation, and how is it found?

The x-intercept is the point where the line crosses the x-axis, and it provides additional information about the line. The x-intercept is found by plugging in y = 0 into the equation. Signup and view all the answers

Match the following forms of linear equations with their characteristics:

Slope-intercept form = Easy to graph and find the y-intercept Point-slope form = Useful when given a point and the slope Standard form = Useful for systems of linear equations Graphing method = Not a form of linear equation Signup and view all the answers

Match the following types of slopes with their descriptions:

Positive slope = Line slopes upward from left to right Negative slope = Line slopes downward from left to right Zero slope = Horizontal line Undefined slope = Vertical line Signup and view all the answers

Match the following graphing methods with their formulas:

Slope-intercept form = y = mx + b Point-slope form = y - y1 = m(x - x1) Standard form = Ax + By = C Graphing method = Not a formula Signup and view all the answers

Match the following characteristics with the types of lines:

Parallel lines = Have the same slope (m) and never intersect Perpendicular lines = Have slopes that are negative reciprocals of each other and intersect at a right angle Horizontal line = Zero slope Vertical line = Undefined slope Signup and view all the answers

Match the following steps with the process of graphing a linear equation:

Find the y-intercept (b) = Step 1 Use the slope (m) to find another point on the line = Step 2 Draw the line through the two points = Step 3 Find the x-intercept = Not a step in graphing a linear equation Signup and view all the answers

Match the following characteristics with the forms of linear equations:

Slope-intercept form = Useful for graphing and finding the y-intercept Point-slope form = Useful when given a point and the slope Standard form = Useful for systems of linear equations and not for graphing Graphing method = Not a form of linear equation Signup and view all the answers

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Study Notes

Linear Equations in Two Variables

A linear equation in two variables is an equation that can be written in the form:
- Ax + By = C
- Where A, B, and C are constants, and A and B are not both zero
The graph of a linear equation in two variables is a straight line
Solutions to the equation are the points (x, y) that satisfy the equation

Slope of a Line

The slope of a line is a measure of how steep it is
Slope is denoted by the letter m and is calculated as:
- m = (y2 - y1) / (x2 - x1)
- Where (x1, y1) and (x2, y2) are two points on the line
Slope can be positive, negative, zero, or undefined
A positive slope indicates a line that rises from left to right
A negative slope indicates a line that falls from left to right
A zero slope indicates a horizontal line
An undefined slope indicates a vertical line

Graphing Linear Equations

To graph a linear equation, start by plotting the y-intercept (the point where the line crosses the y-axis)
Use the slope to find additional points on the line
Plot the additional points and draw a straight line through them
The x-intercept (the point where the line crosses the x-axis) can be found by plugging in x = 0 into the equation

Forms of the Equation of a Line

There are three main forms of the equation of a line:
1. Slope-Intercept Form: y = mx + b
  - Where m is the slope and b is the y-intercept
2. Point-Slope Form: y - y1 = m(x - x1)
  - Where (x1, y1) is a point on the line and m is the slope
3. Standard Form: Ax + By = C
  - Where A, B, and C are constants, and A and B are not both zero

Slopes of Parallel and Perpendicular Lines

Parallel Lines: lines that never intersect and have the same slope
- If two lines are parallel, their slopes are equal
Perpendicular Lines: lines that intersect at a right angle (90 degrees) and have slopes that are negative reciprocals
- If two lines are perpendicular, their slopes are negative reciprocals of each other
If the slope of one line is m, the slope of a parallel line is also m, and the slope of a perpendicular line is -1/m