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Core Focus on Linear Equations

Lesson 3.1. Core Focus on Linear Equations. Graphing Using Slope-Intercept Form. Warm-Up. Determine the slope and y -intercept for each linear equation. y = 2 + 4 x y = x – 5 y = – x + 1 y = 3. Slope: 4 y -intercept: 2. Slope: y -intercept: –5. Slope: y -intercept: 1.

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Core Focus on Linear Equations

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  1. Lesson 3.1 Core Focus onLinear Equations Graphing Using Slope-Intercept Form

  2. Warm-Up Determine the slope and y-intercept for each linear equation. • y = 2 + 4x • y = x – 5 • y = – x + 1 • y = 3 Slope: 4 y-intercept: 2 Slope: y-intercept: –5 Slope: y-intercept: 1 Slope: 0 y-intercept: 3

  3. Lesson 3.1 Graphing Using Slope-Intercept Form Graph linear equations in slope-intercept form.

  4. Vocabulary Slope-Intercept Form Linear equation written in the form y = mx + b. Good to Know! Slope-intercept form is the most common equation used to represent a linear function. It is called this because the slope and the y-intercept are easily identified.

  5. Slope-Intercept Form of a Linear Equation y = mx + b The slope of the line is represented by m. The y-intercept is b.

  6. Good to Know!  Slope (m) is also called the rate of change. The slope gives you the rise over the run of the line.  The y-intercept is also called the start value. The y-intercept is the location the line crosses the y-axis. The ordered pair for the y-intercept will be (0, b).  Equations in slope-intercept form may also be written y = b + mx.

  7. Example 1 Graph y = x – 2. Clearly mark at least 3 points on the line. First determine the slope and y-intercept. y = x – 2 m = b = –2 Start by graphing the y-intercept on the coordinate plane. Use the slope to find at least two more points. Draw a straight line through the points. Put an arrow on each end. slope y-intercept Remember rise over run!

  8. Example 2 The slope is the coefficient of x Graph each linear equation. Clearly mark at least three points on each line. a. y = 6 – 2x m = –2 and b = 6 Graph the y-intercept of 6 and then graph 3 points using the slope fraction –2 = . Draw a straight line through the points. Put an arrow on each end. y-intercept

  9. Example 2 Continued… Graph each linear equation. Clearly mark at least three points on each line. b. y = x + 1 m = and b = 1 Sometimes you may have to use your slope in two directions. Go down 7 and right 2. In order to get another point on the coordinate plane, go up 7 and left 2.

  10. Good to Know! As you learned in Block 2, there are lines that have a slope of zero and other lines that have an undefined slope. The equations of these lines are unique. Zero Slope Undefined Slope y = constant x = constant y = 2 x = –1

  11. Vocabulary Continuous A graph which can be drawn from beginning to end without lifting your pencil.  Continuous graphs often represent real-world scenarios where something is happening continuously with no breaks.  A graph can be continuous but limited to a certain quadrant or section of the graph. Example: Lamar types 40 words per minute. It would not make sense to graph points out of the first quadrant because he cannot type for a negative number of minutes or type a negative number of words.

  12. Vocabulary Discrete A graph that can be represented by a unique set of points rather than a continuous line.  Some situations are modeled by linear equations but are not continuous. This could mean that it would not make sense to connect the points of the equation with a line. Example: Jenna started with $50 in her savings account. She adds $10 each month. The linear equation that represents her balance is y = 50 + 10x. Since she only puts money in her account once a month, a line should not be drawn through the points on the graph.

  13. Communication Prompt How can you tell if a line is going to be a vertical line or a horizontal line based on its equation?

  14. Exit Problems Graph each linear equation. Clearly mark at least three points on each line. 1. y = x – 1 2. y = 4 – 3x 3. y = –1

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