## Key Concepts

• Linear functions may be graphed by plotting points or by using the y-intercept and slope.
• Graphs of linear functions may be transformed by using shifts up, down, left, or right, as well as through stretches, compressions, and reflections.
• The y-intercept and slope of a line may be used to write the equation of a line.
• The x-intercept is the point at which the graph of a linear function crosses the x-axis.
• Horizontal lines are written in the form, f(x) = b.
• Vertical lines are written in the form, = b.
• Parallel lines have the same slope.
• Perpendicular lines have negative reciprocal slopes, assuming neither is vertical.
• A line parallel to another line, passing through a given point, may be found by substituting the slope value of the line and the x– and y-values of the given point into the equation, $f\left(x\right)=mx+b\\$, and using the b that results. Similarly, the point-slope form of an equation can also be used.
• A line perpendicular to another line, passing through a given point, may be found in the same manner, with the exception of using the negative reciprocal slope.
• A system of linear equations may be solved setting the two equations equal to one another and solving for x. The y-value may be found by evaluating either one of the original equations using this x-value.
• A system of linear equations may also be solved by finding the point of intersection on a graph.

## Glossary

horizontal line
a line defined by $f\left(x\right)=b\\$, where b is a real number. The slope of a horizontal line is 0.
parallel lines
two or more lines with the same slope
perpendicular lines
two lines that intersect at right angles and have slopes that are negative reciprocals of each other
vertical line
a line defined by x = a, where a is a real number. The slope of a vertical line is undefined.
x-intercept
the point on the graph of a linear function when the output value is 0; the point at which the graph crosses the horizontal axis