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.