Points with a y-coordinate equal to 0 are on the x-axis, and have coordinates ( a, 0).
Points with a x-coordinate equal to 0 are on the y-axis, and have coordinates ( 0, b).
The point (0, 0) is called the origin. It is the point where the x-axis and y-axis intersect.
11.2 Graphing Linear Equations
Graph a linear equation by plotting points.
Step 1. Find three points whose coordinates are solutions to the equation. Organize them in a table.
Step 2. Plot the points on a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work.
Step 3. Draw the line through the points. Extend the line to fill the grid and put arrows on both ends of the line.
Graph of a Linear Equation:The graph of a linear equation ax+by=cax+by=c is a straight line.
Every point on the line is a solution of the equation.
Every solution of this equation is a point on this line.
11.3 Graphing with Intercepts
Intercepts
The x-intercept is the point, (a,0)(a,0), where the graph crosses the x-axis. The x-intercept occurs when y is zero.
The y-intercept is the point, (0,b)(0,b), where the graph crosses the y-axis. The y-intercept occurs when x is zero.
The x-intercept occurs when y is zero.
The y-intercept occurs when x is zero.
Find the x and y intercepts from the equation of a line
To find the x-intercept of the line, let y=0y=0 and solve for x.
To find the y-intercept of the line, let x=0x=0 and solve for y.
Graph a line using the intercepts
Step 1. Find the x- and y- intercepts of the line.
Let y=0y=0 and solve for x.
Let x=0x=0 and solve for y.
Step 2. Find a third solution to the equation.
Step 3. Plot the three points and then check that they line up.
Step 4. Draw the line.
Choose the most convenient method to graph a line
Step 1. Determine if the equation has only one variable. Then it is a vertical or horizontal line. x=ax=a is a vertical line passing through the x-axis at a. y=by=b is a horizontal line passing through the y-axis at b.
Step 2. Determine if y is isolated on one side of the equation. The graph by plotting points. Choose any three values for x and then solve for the corresponding y- values.
Step 3. Determine if the equation is of the form Ax+By=CAx+By=C, find the intercepts. Find the x- and y- intercepts and then a third point.
Find the slope from a graph
Step 1. Locate two points on the line whose coordinates are integers.
Step 2. Starting with the point on the left, sketch a right triangle, going from the first point to the second point.
Step 3. Count the rise and the run on the legs of the triangle.
Step 4. Take the ratio of rise to run to find the slope, m=rise/run
Slope of a Vertical Line
The slope of a vertical line, x=ax=a, is undefined.
Graph a line given a point and a slope.
Step 1. Plot the given point.
Step 2. Use the slope formula to identify the rise and the run.
Step 3. Starting at the given point, count out the rise and run to mark the second point.