# Key Concepts & Glossary

## 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,
*x*=*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, [latex]f\left(x\right)=mx+b\\[/latex], 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 [latex]f\left(x\right)=b\\[/latex], 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

## Licenses & Attributions

### CC licensed content, Shared previously

- Precalculus.
**Provided by:**OpenStax**Authored by:**Jay Abramson, et al..**Located at:**https://openstax.org/books/precalculus/pages/1-introduction-to-functions.**License:**CC BY: Attribution.**License terms:**Download For Free at : http://cnx.org/contents/[email protected]..