Mathematics Module 4: Graphing Linear Equations

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Questions and Answers

Which of the following statements is true about graphing linear equations?

  • Linear equations can be graphed using slopes and points. (correct)
  • Graphing requires the use of x- and y-intercepts only.
  • Graphs of linear equations are always curved.
  • You can only graph two points at a time.

Which ordered pair satisfies the equation $x + y = 5$?

  • (3, 2)
  • (2, 2)
  • (1, 4) (correct)
  • (3, 3)

Which of the following actions should be avoided while using the module?

  • Reviewing answers before finishing a task.
  • Using the module to practice additional exercises.
  • Skimming through the module without engagement. (correct)
  • Taking notes in a separate notebook.

What is the slope of the line represented by the equation $2y = -x + 6$?

<p>-2 (A)</p> Signup and view all the answers

What are the coordinates of the y-intercept for the equation $y = -2x + 3$?

<p>3 (B)</p> Signup and view all the answers

When graphing the line with equation $y = -2x + 3$, what is the next point one could plot after the y-intercept?

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Which step is NOT part of graphing linear equations using given points?

<p>Assign values for y to solve for x (D)</p> Signup and view all the answers

What figure is formed when connecting the points A (4, 3), B (-3, 2), C (3, -1), D (0, 5), and E (-2, -2) in consecutive order?

<p>Pentagon (B)</p> Signup and view all the answers

Which equation represents a linear equation suitable for graphing using two points?

<p>y = 3x + 2 (A)</p> Signup and view all the answers

If the equation x + 2y = 4 is solved for y, what is the resulting equation?

<p>y = - rac{1}{2}x + 2 (B)</p> Signup and view all the answers

What method can be used to find the coordinates of points on the graph of a linear equation?

<p>Using the slope and a point on the line (B)</p> Signup and view all the answers

What is the graph of the equation 3x - y = 3?

<p>A line with a positive slope (A)</p> Signup and view all the answers

Which point is on the line represented by x + y = 2?

<p>(0, 2) (A), (2, 0) (B), (1, 1) (D)</p> Signup and view all the answers

What does the slope of a line indicate?

<p>How steep the line is and the direction it goes (D)</p> Signup and view all the answers

For the equation y = 3x - 1, what is the y-intercept?

<p>-1 (B)</p> Signup and view all the answers

How do you find the x-intercept of the line represented by 3x + y = 3?

<p>Set y to 0 and solve for x (A)</p> Signup and view all the answers

In graphing linear equations, what does a horizontal line indicate about its slope?

<p>The slope is zero (B)</p> Signup and view all the answers

If the slope of a line is negative, how does the line behave as it moves from left to right?

<p>Decreases (D)</p> Signup and view all the answers

What is the trend of the graph of a linear equation whose slope is negative?

<p>falls from left to right (C)</p> Signup and view all the answers

Which of the following points passes through the equation $3x + y = -3$?

<p>(-1, 0) (A)</p> Signup and view all the answers

What will be the first point to be located on the graph of the equation $y = 3x - 2$ using the y-intercept?

<p>(0, -2) (D)</p> Signup and view all the answers

What is the trend of the graph of the linear equation $y = 3x + 5$?

<p>increases from left to right (C)</p> Signup and view all the answers

What is the slope of the equation $x - 3y = 6$?

<p>-3 (C)</p> Signup and view all the answers

Which equation best describes a line that intercepts the y-axis at 1 and slopes downward?

<p>y = -x + 1 (C)</p> Signup and view all the answers

What will the trend of the graph look like based on Criz's candle experiment?

<p>decreasing (B)</p> Signup and view all the answers

If the candle burns at a constant rate, how long will it take to use up the entire 8 inches of candle?

<p>4 hours (A)</p> Signup and view all the answers

What is a characteristic of graphs that decreases from left to right?

<p>The slope is negative. (C)</p> Signup and view all the answers

If a linear equation is graphed and the y-intercept is 2, what does this indicate?

<p>The line crosses the y-axis at 2. (A)</p> Signup and view all the answers

Which of the following measures time in hours?

<p>4 hours (D)</p> Signup and view all the answers

What can be inferred if a learner states 'the graph increases from left to right'?

<p>The slope is positive. (B)</p> Signup and view all the answers

What does a line in slope-intercept form primarily consist of?

<p>A slope and a y-intercept. (C)</p> Signup and view all the answers

If a graph has a slope of zero, what type of line does it represent?

<p>A horizontal line. (B)</p> Signup and view all the answers

Which of the following is true regarding intercepts in a linear graph?

<p>They are points where the graph crosses the axes. (C)</p> Signup and view all the answers

What is typically the first step in graphing a linear equation?

<p>Identifying the y-intercept. (B)</p> Signup and view all the answers

What is the trend of the graph represented by the equation y = -2x + 3?

<p>Decreasing from left to right (D)</p> Signup and view all the answers

Which point can be plotted next after the y-intercept (0, 3) using the slope of -2?

<p>(-2, 4) (D)</p> Signup and view all the answers

For the equation x + 2y = 6, when graphed, how does the graph behave as it approaches the x-axis?

<p>It approaches horizontally (D)</p> Signup and view all the answers

What does the graph of the equation y = -3 look like?

<p>A horizontal line (D)</p> Signup and view all the answers

Which of the following statements about the equation x = 5 is true?

<p>It has an undefined slope (D)</p> Signup and view all the answers

When graphing the equation y = -2x + 3, what is the correct first step?

<p>Plot the y-intercept (0, 3) (D)</p> Signup and view all the answers

What is a characteristic of the line represented by the equation y = -2x + 3?

<p>It crosses the y-axis at (0, 3) (C)</p> Signup and view all the answers

What are the coordinates of the y-intercept for the linear equation y = -2x + 3?

<p>(0, 3) (D)</p> Signup and view all the answers

Flashcards

Graphing linear equations

Representing linear equations visually on a coordinate plane

Coordinate plane

A two-dimensional plane used to graph points and lines. Points are represented by ordered pairs (x, y).

Ordered pair

A pair of numbers (x, y) that locate a point on a coordinate plane.

X-intercept

The point where a graph crosses the horizontal x-axis; The y coordinate is zero when (x, y) is on the x-axis.

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Y-intercept

The point on a graph where a line crosses the vertical y-axis; the x coordinate is zero when (x,y) is on the y-axis.

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Linear equation in two variables

An equation that can be graphed as a straight line on a coordinate plane.

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Slope

The steepness of a line; the rate of change between y and x coordinates.

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Graphing points

Plotting ordered pairs (x,y) on a coordinate plane.

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Linear Equation

An equation that forms a straight line when graphed.

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Method of graphing linear equation using two points

Graphing a linear equation by plotting two points that satisfy the equation and drawing a straight line through them.

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Positive Slope

A line that slopes upward from left to right. Its slope value ('m') is positive.

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Negative Slope

A line that slopes downward from left to right. Its slope value ('m') is negative.

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Slope-Intercept Form

The standard form of a linear equation is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

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Graphing a Line with Slope and Intercept

You can graph a line using its slope and y-intercept. Start at the y-intercept and use the slope to find additional points.

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Horizontal Line

A horizontal line has a slope of 0 and has the form y = c, where 'c' is the y-intercept.

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Vertical Line

A vertical line has an undefined slope and has the form x = c, where 'c' is the x-intercept.

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Graphing a Line Given Two Points

You can graph a line by plotting two points on the coordinate plane and drawing a line that connects them.

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Finding the Equation of a Line Given Two Points

You can find the equation of a line given two points by first finding the slope using the slope formula, then using the point-slope form to create the equation.

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Negative slope's trend

The graph of a linear equation with a negative slope decreases from left to right.

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Point on a line

A point lies on the graph of a linear equation if its coordinates satisfy the equation.

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Y-intercept of equation

The y-intercept of a linear equation in the form y = mx + c is the point (0, c), where c is the constant term.

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Positive slope's trend

The graph of a linear equation with a positive slope increases from left to right.

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Slope of a line equation

To find the slope of a linear equation in the form ax + by = c, solve for y to get y = mx + c, where m is the slope.

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Graph of a linear equation

The graph of a linear equation is a straight line representing all the points that satisfy the equation.

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Matching a graph to an equation

To find the equation of a line from its graph, identify the slope and y-intercept, then plug them into the slope-intercept form (y = mx + c).

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Equation of a line from a graph

The equation of a line is a mathematical representation of its relationship between x and y coordinates. Using the slope-intercept form (y = mx + c) can determine the equation.

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Slope of a Line

The steepness of a line; the rate of change between the y and x coordinates.

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Graphing by Two Points

Plotting two points that satisfy a linear equation and drawing a straight line through them to represent the equation visually.

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What does the slope of a line tell you?

The rate of change between the y and x coordinates; how steep the line is.

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How do you find the y-intercept of a linear equation?

The y-intercept is the constant term 'c' in the equation y = mx + c.

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Study Notes

Mathematics Module 4: Graphing Linear Equations

  • Topic: Graphing linear equations given two points, x- and y-intercepts, and slope and a point on the line. Also, describing the graph of linear equations.
  • Target Audience: Grade 8 Students
  • Module Focus: This module guides students through methods to graph equations.
  • Methods: Graphing linear equations can be done by plotting given two points, using x- and y-intercepts, or using the slope and a point on the line.
  • Learning Outcomes: Students will gain skills in graphing linear equations, identifying x-and y-intercepts, and interpreting the slope of a line.
  • Important Concepts: Slope-intercept form (y = mx + b) is key. Slope indicates the direction and steepness of a line. Y-intercept is the point where the line crosses the y-axis. X-intercept is the point where the line crosses the x-axis.

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