Section 5 -1 CC Rate of Change and Slope.
Objectives:
To find rates of change from tables and graphs.
To find slope.
Rate of Change: allows you to see the relationship between two quantities that are changing.
Rate of change = change in the dependent variable
Change in the independent variable
Slope: describes the steepness of a line.
Slope = vertical change = rise = y 2 – y 1
horizontal change run x2 – x1
Slope = rate of change
Section 5-2 CC: Direct Variation.
Objectives:
To write and graph an equation of a direct variation.
Direct Variation: a function in the form of
y = kx where k ≠ 0 .
A direct variation is a Linear Function.
The graph of a direct variation always passes through the origin.
y varies directly with x .
Constant of Variation: the coefficient of x.
k is the constant of variation.
k = y
x
k is written as an Integer or a Fraction.
* Use the ratio y/x to determine if a table of values
is a direct variation.
* Use the proportion x 1 = x 2
y1 y2
to find the missing coordinate of a direct variation.
Section 5-3 CC: Slope - Intercept Form.
Objectives:
To write equations in slope-intercept form.
To graph linear equations in slope-intercept form.
Linear Equation: an equation that models a linear function.
y – intercept: the y-coordinate of the point where a line crosses the y-axis.
x – intercept: the x-coordinate of the point where a line crosses the x-axis.
Slope – Intercept Form of a Linear Equation:
y = mx + b
m = slope b = y-intercept
Characteristics of Horizontal & Vertical Lines:
Horizontal Lines:
Slope → m = 0
Equation → y = y-intercept
Points → the points on a Horizontal line have
the same y-coordinates
( 3 , 1) (-2 , 1) .
Vertical Lines:
Slope → No Slope/Undefined
Equation → x = x-intercept
Points → the points on a Vertical line have
the same x-coordinates
( 2 , 4 ) ( 2 , - 5) .
TI-83 Graphing Calculator Procedures For:
Writing the Equation of a Line Given:
1) Two Coordinates:
STAT - EDIT - ENTER -
enter the x-coordinates under the L1column and y-coordinates under the L2 column -
STAT - CALC - #4 LinReg - ENTER -
ENTER.
a = slope, b = y-intercept for y = ax + b.
2) A Table of Values:
SAME AS ABOVE.
Section 5-4 CC: Point – Slope Form
Objectives:
To graph and write linear equations using point-slope form.
Point – Slope Form: is a FORMULA to write a linear equation.
Point – Slope Form: y - y1 = m ( x - x1 )
m → slope
x1 → x-coordinate of the point.
y1 → y-coordinate of the point.
Section 5-5 CC: Standard Form.
Objective:
To graph equations using intercepts.
To write linear equations in standard form.
Standard Form of a Linear Equation:
Ax + By = C or - Ax – By = - C
Multiply every term by the LCD to clear out any fractions if necessary.
Move the term with x to the left side of the equation.
Move the term with y to the left side of the equation.
Move the constant to the right side of the equation.
To Find the x-intercept:
Substitute 0 in for y and solve the equation.
To Find the y-intercept:
Substitute 0 in for x and solve the equation.
Sec tion 5-6 CC: Parallel and Perpendicular Lines.
Objectives:
To write the equations of parallel and perpendicular lines.
To determine if lines are parallel or perpendicular.
Parallel Lines: two lines that never intersect.
Parallel lines have the same slope but different
y-intercepts.
Perpendicular Lines: lines that intersect to form right angles.
Two lines are perpendicular if the product of their slopes is - 1 .
Opposite Reciprocal s : the opposite and the reciprocal of a number.
· Two horizontal lines are parallel.
· Two vertical lines are parallel.
· A horizontal line and a vertical line are perpendicular.
Section 5-7 Scat ter Plots and Trend Lines .
Objectives:
To write an equation for a trend line and use it to make predictions.
To use a line of best fit to make predictions.
Scatter Plot: a graph that relates two different sets of data by displaying them as ordered pairs.
Line of Best Fit: (trend line) is a line on a scatter plot, drawn near the points, that shows a correlation.
Interpolation: estimating a vale between two known values.
Extrapolation: predicting a value outside the range of known values.
Positive Correlation: two sets of data increase together.
Negative Correlation: One set of data increases as the other decreases.
No Correlation: two data sets are not related.
Causation: when a change in one quantity causes a change in a second quantity.
Writing the Equation of a Trend Line and Finding the Correlation:
2ND - 0 CATALOG - Scroll down to DIAGNOSTIC ON - ENTER - ENTER.
STAT - EDIT - ENTER - enter the x-coordinates under the L1and y-coordinates under the L2
STAT - CALC - #4 LinReg - ENTER - ENTER.
a = slope, b = y-intercept for y = ax + b.
r = correlation coefficient
Strong No Correlation Strong
----------------------------------------------------------------
-1 0 1
Strong Correlation:
0.5 to 1 & - 0.5 to - 1
No Correlation:
0.49 to - 0.49
Section 5-8 CC: Graphing Absolute Value Equations.
Objective:
To graph an absolute value function.
To translate the graph of an absolute value function.
Absolute Value Equation: a V – shaped graph that opens upward or downward.
Translation: is a shift of a graph horizontally, vertically or both.
│x + 2 │ → shifts left 2
│ x – 2 │→ shifts right 2
│x │ + 2 → shifts up 2
│x │ - 2 → shifts down 2