Algebra Notes
Chapter 4 – Equations of Linear Functions
4.1 Graphing Equations in Slope-Intercept Form
Slope-Intercept Form – An equation of the form:
y  mx b , where m is the slope and b is
the y-intercept of a given line.
Constant Function – A linear function of the form
Identity Function – The function
y x
y b
. This is also known as the parent function.
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4.2 Writing Equations in Slope-Intercept Form
Constraint – A condition that a solution must satisfy. Equations can be viewed as constraints in
a problem situation. The solutions of the equation meet the constraints of the problem.
Linear Extrapolation – The use of a linear equation to predict values that are outside the range
of data.
4.3 Writing Equations in Point-Slope Form
Point-Slope Form – For any given point (X,Y) on a non-vertical line having slope M, the pointslope form of a linear equation is as follows:
y y = m(x x )
1
1
Standard Form – The standard form of a linear equation is: Ax  By C , where A, B and C
are integers, A  0, and A and B are not both zero
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4.4 Parallel and Perpendicular Lines
Parallel Lines – Lines in the plane that never intersect. Non-vertical parallel lines have the
same slope. Same slope equals parallel lines!
Perpendicular Lines – Lines that meet to form right angles. Two slopes that multiply to be -1
are considered perpendicular lines. Think… opposite reciprocals!
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4.5 Scatter Plots and Lines of Fit
Bivariate Data – Data with two variables
Scatter Plot – In a scatter plot, the two sets of data are plotted as ordered pairs in the coordinate
plane
Line of Fit – A line that describes the trend of data.
Linear Interpolation – The use of a linear equation to predict values that are inside of the data
range.
Positive Correlation – There is a positive correlation between x and y if the values are related in
the same way
Negative Correlation - There is a negative correlation between x and y if the values are related
in opposite ways
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4.6 Regression and Median-Fit Lines
Best-fit Line – A line drawn on a scatter plot that passes close to most of the data points
Linear Regression – An algorithm to find a precise line of fit for a set of data.
Correlation Coefficient – A value that shows how close data points are to a line.
Residual – The difference between an observed y-value and its predicted y-value on a regression
line.
Median Fit Line – A type of best fit line that is calculated using the medians of the coordinates
of the data points.
4.7 Inverse Linear Functions
Inverse Relation – The set of ordered pairs obtained by exchanging the x-coordinates with the
y-coordinates of each ordered pair in a relation. If (5,3) is an ordered pair of a relation, then
(3.5) is an ordered pair of the inverse relation.
Inverse Function – The inverse of the linear function f (x ) can be written as f 1 ( x) and is read
“ f of x inverse” or “the inverse of f of x”
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