Chapter 7 Graphing Linear Equations REVIEW

Section 7.1 Cartesian Coordinate System is formed by two axes drawn perpendicular to each other. Origin is the points of intersection for the x- and y-axis (0, 0) Horizontal axis is the x-axis Vertical axis is the y-axis Ordered Pairs are of the form of (x, y)

Section 7.1 Linear Equations in two variables is an equation that can be put in the form ax 2 + bx = c where a, b and c are real numbers. Also called standard form A Graph of an equation is in two variables is an illustration of a set of points whose coordinates satisfy the equation Collinear points are point that lie in a straight line Non-collinear points are not on the line

Section 7.2 Graphing Linear Equations by Plotting Points Solve the linear equation for y Select a value for x and substitute in the equations to find a value for y Select two additional values for x and find two additional values for y Plot the three ordered pairs Draw a straight line with arrows on the ends through the three points

Section 7.2 x-intercept is the point where the graph crosses the x-axis y-intercept is the point where the graph crosses the y-axis Horizontal Line Graph is in the form of y = b y-intercept is (0, b) Slope is 0 Vertical Line Graph is in the form of x = a x-intercept is (a, 0) Slope is undefined

Section 7.2 Graphing Linear Equations using x- and y-intercept Find y-intercept by setting x equal to 0 Find x-intercept by setting y equal to 0 Determine a checkpoint with a non-zero value for x and find the corresponding y Plot the x- and y-intercept and the checkpoint Draw a straight line with arrows on the ends through the three points

Section 7.3 Slope of the Line is the ratio of the vertical change to the horizontal change between two selected points on the line. Positive Slope is a straight line where the value of y increases as x increases. Negative Slope is a straight line where the value of y decreases as x increases.

Section 7.3 Parallel Lines – two nonvertical lines with the same slope and different y-intercepts Any two vertical lines are parallel Perpendicular Lines – two lines whose slopes are negative reciprocals of each other Any vertical line is perpendicular to any horizontal line

Section 7.4 Slope-intercept Form of a linear equation y = mx + b where m is the slope, and (0, y) is the y-intercept of the line To graph ac + by = c, write the equation in slope-intercept form by solving the equation for y. Then use the slope and y-intercept to sketch the graph. Point-Slope Form of a linear equation y – y 1 = m(x – x 1 ) where m is the slope of the line and (x 1, y 1 ) is a point on the line.

Section 7.5 Linear inequality occurs when the equal sign in a linear equation is replaced with an inequality sign ≤ ≥ To graph in Linear Inequality in Two Variables 1. Replace the inequality with an equal sign 2. Draw a graph of the equation. If symbol is ≥ or ≤ draw a solid line If symbol is > or < draw a dotted line 3. Select a point not on line. If solution shade the region If not a solution shade the side not containing the points

Section 7.6 Relation is any set of ordered pairs Function is a set of ordered pairs in which each first component corresponds to exactly one second component Domain of a relation or function is the set of first components in the set of ordered pairs Range of a relation or function is the set of second components on the set of ordered pairs

Section 7.6 Vertical Line Test A vertical line can be drawn through any part of a graph and the vertical line intersects another part of the graph. The graph is not a function A vertical line cannot be drawn to intersect the graph at more than one point. The graph is a function Function Notation is f(x) y = mx + b is a linear equation f(x) = mx + b is a linear function