Linear Equations and Their Graphs

1
Linear Equations and Their Graphs

• Slope, Points, and Lines

2
Rate of Change and Slope

• Rate of Change (change in dependent variable) /
  (change in independent variable)
• For a line (vertical change/horizontal change)
• Slope Rate of Change (difference in
  ys)/(difference in xs) rise/run
• Memorize formula on page 284!!!
• Horizontal Lines have a slope of Zero, and
  Vertical Lines have a slope that is Undefined.
• A positive slope means that the line slants
  upward from left to right, and a negative slope
  means that the line slants downward from left to
  right.

3
Linear Equations

• Three forms Standard, Point-Slope, and
  Slope-Intercept.
• Y-intercept is the point where the line crosses
  the y axis.
• X-intercept is the point where the line crosses
  the x axis.
• Y mx b is slope intercept form. It is very
  easy to graph from because b is the y- intercept,
  and m is the slope between points on the line.

4
Standard Form

• Ax By C is standard form, but A and B cannot
  both be zero at the same time.
• You can find the X-intercept by substituting zero
  in for y, and solving for x. You can also find
  the Y-intercept by substituting zero in for x,
  and solving for y.
• You can graph a line using its intercepts, they
  represent two points on the line.

5
Point-Slope Form and Writing Linear Equations

• It is easiest to write an equation using this
  form. If you know a slope and a point, then you
  can put x and y in for y1, and x1, likewise you
  can put the slope in for m.
• If you know two points, you can calculate the
  slope and follow the same procedure using one of
  the points you know.
• Memorize the Chart on Page 307 with examples of
  each form.

6
Parallel and Perpendicular Lines

• Parallel lines never intersect because they have
  the same slope, but different y-intercepts.
• You can usually tell from slope-intercept form if
  two lines are parallel.
• Perpendicular Lines intersect at a right angle
  because they have negative reciprocal slopes.
  Vertical and Horizontal lines are also
  perpendicular.

7
Scatter Plots and Equations of Lines

• The line of best fit is a line that best
  estimates the trend of a set of data points.
• A graphing calculator can help you find the line
  of best fit using the LinReg function.

8
Graphing Absolute Value Functions

• A V-shaped graph that opens upward or downward is
  the absolute value equation.
• Translations (shifts) of the absolute value
  function can be found by looking at the number
  inside the abs bars, and outside the abs bars.
• If there is a negative in front of the bars, the
  graph opens downward.
• If there is a number inside the bars, the sign
  determines left or right neg right, and pos
  left.
• If there is a number behind the bars, then the
  sign determines whether the graph shifts up or
  down neg down, and pos up.