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Refresher NOTES
Date _____________
Graphing and Writing Linear Equations
vertical change (rise) (y – y)
horizontal change (run) (x – x)
A line with a positive slope goes upward from left to right.
A line with a negative slope goes downward from left to right.
The slope of a horizontal line is zero.
The slope of a vertical line is undefined.
SLOPE =
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Rates of Change =
Change in the dependent variable (y)
Change in the independent variable (x)
 The graph of a linear function is a line. The rate of change between
consecutive pairs of data in a table is constant.
Slope-Intercept Form
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The point where a line crosses the y-axis is the y-intercept.
The coefficient of x is equal to the slope.
The greater the coefficient the steeper the line.
The slope-intercept form of a linear equation is y = mx + b, where m is the
slope and b is the y-intercept.
Example 1: You can use the slope and the y-intercept to graph an equation.
Example 2: You may need to rewrite a linear equation to express it in slopeintercept form.
Rewrite y – 5 = 4x in slope-intercept form.
Example 3: You can use the equation of a line to determine if a point lies on the
line.
Writing the Equation of a Line
In some real-world situations you can identify the rate of change, or slope, and
an ordered pair. Then you can use the slope and ordered pair to model the
situation with a linear equation.
You can use two points on a line to find and equation for the line. First find the
slope of the line through the two points. Then use the slope and one point to find
the y-intercept and to write an equation of the line.
You can also write a linear equation for data in tables. Two sets of data have a
linear relationship if the rate of change between consecutive pairs of data is the
same.
Parallel and Perpendicular Lines
Parallel lines are always the same distance apart. They do not intersect. Vertical
lines are parallel (and their slope is undefined). Horizontal lines are parallel (and
their slope is zero). Non vertical lines are parallel if they have the same slope and
different y-intercepts.
EX. The slope of y = 2x + 3 and y = 2x – 5 is 2. The graphs of these two
equations are parallel.
You can use slope to write an equation of a line parallel to a given line.
EX. Write an equation for a line that contains (-2,3) and is parallel to the graph of
5x -2y = 8.
1st find the slope by writing the equation in y-intercept form
2nd use the slope and the point to solve for b(y-intercept)
3rd now write the parallel equation
Perpendicular lines are lines that form right angles. The slopes of perpendicular
lines also have a special relationship.
Two lines are perpendicular is the product of their slopes is -1. (reciprocal and
opposite sign)
EX. The slope of y = -4x + 7 is -4. The slope of y = 1/4x + 2 is ¼.
Since -4 times ¼ = -1, the graphs of the equations are perpendicular.
EX. Find the slope of a line perpendicular to the graph of each equation. If the
equation is not in slope-intercept form, transform it to find the slope.
y = 2x
y = -x/5 – 7
2x + 3y = 5
4x – 2y = 9
x=3
y = -8
Write an equation for a line that satisfies the given conditions.
EX. Perpendicular to
y = -1/2x + 4, through (-3, 5)
EX. Parallel to y = 4x – 7, through (5, -1)