Algebra Concepts Chapter 3 Notes Note: We will only cover sections 3-1 and 3-3

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

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)

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

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 = 16b) -3x + 12y = 24

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

Section 3-1: Graphing using a table Steps: 1)Make a _______ 2)Fill in the ______’s with any values use choose (Hint: use easy values) 3)Plug each ______ into the equation to find ______ 4)Fill in the table with the _______

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

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 Number of Computer Games Total Cost ($) xy

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 Number of Computer Games Total Cost ($) xy

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

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

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

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

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

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

Section 3-3: Slope Positive SlopeNegative Slope Slope of 0Undefined Slope

Section 3-3: Slope Ex) Find the value of r so that the line through a) (1, 4) and (-5, r) has a slope of 1/3 b) (-2, 8) and (r, 4) has a slope of ½