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Comprehensive Basic Algebra: Linear Equations Graphing & Slope Formulas

Learn how to graph linear equations in standard form, find intercepts, calculate slope, and understand rate of change. Includes graphing methods and slope formulas with examples.

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Comprehensive Basic Algebra: Linear Equations Graphing & Slope Formulas

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  1. Basic Algebra Chapter 3 Notes

  2. Section 3-1 Graphing Linear Equations Linear Equation – Standard Form – Constant -

  3. Section 3-1 Graphing Linear Equations Linear Equation – an equation that forms a line when graphed Standard Form – a linear equation written in the form Ax + By = C, where A and B cannot both be zero and C is a constant Constant – a number (no variable)

  4. Section 3-1 Ex. 1) Determine if the equation is linear. Write the equation in standard form. • y = 4 – 3x b) 6x – xy = 4

  5. Section 3-1: Finding the x and y intercepts Ex) Find the x and y intercepts of the following equations 1) Plug ________ in for ____ and solve for ____ 2) Plug ________ in for ____ and solve for ____ a) 2x + 4y = 16 b) -3x + 12y = 24

  6. Section 3-1: Graphing using the intercepts, The “Cover-Up” Method Graph the following equations using the x and y intercepts. a) 2x + 4y = 16 b) -3x + 12y = 24

  7. Section 3-1: Graphing using a table Steps: • Make a _______ • Fill in the ______’s with any values use choose (Hint: use easy values) • Plug each ______ into the equation to find ______ • Fill in the table with the _______

  8. Section 3-1: Graphing using a table Ex) Graph the following equations using a table a) y = 2x – 1 b)

  9. Section 3-3: Rate of Change and Slope Rate of Change – Ex) Use the table to find the rate of change and explain its meaning

  10. Section 3-3: Rate of Change and Slope Rate of Change – If x is the independent variable and y is the dependent variable, then Rate of change = Change in y Change in x Ex) Use the table to find the rate of change and explain its meaning

  11. Section 3-3: Constant Rate of Change Ex) Determine whether each function is linear. a) b)

  12. Section 3-3: Slope Slope – Positive/Negative Slope – Steep vs. Flat –

  13. Section 3-3: Slope Slope – in a non-vertical line, the ratio of the change in y over the change in x, “rise over run”. Positive/Negative Slope – if the slope is positive the line heads to the upper right, if the slope if negative the line heads toward the lower right Steep vs. Flat – the bigger the slope, the steeper the line

  14. Section 3-3: Slope Formula Slope Formula – The slope of any nonvertical line through the points and can be found using the formula: m =

  15. Section 3-3: Slope Ex) Find the slope of a line that passes through the given points • (-2, 0) and (1, 5) b) (-3, 4) and (2, -3) c) (-3, -1) and (2, -1) d) (-4, 2) and (-2, 10)

  16. Section 3-3: Slope Find the slope of the line that passes through (-2, 4) and (-2, -3) Undefined Slope -

  17. Section 3-3: Slope Positive Slope Negative Slope Slope of 0 Undefined Slope

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