Graphing equations on a coordinate plane is a simple way tovisually represent the relationship between the input values (x) ofan equation and the output values (y). This visual representationallows us to make predictions, solve problems, find the point(s)that solve both equations (when there are two), and analyze manyother useful business and everyday situations.
Name some real-life situations where graphing could be useful.Discuss your ideas. Name some real-life situations where findingthe coordinates of the midpoint of a line segment could beuseful.
Choose three non-collinear points on the coordinate plane,making sure none of your points is the origin. On a sheet of paper,graph the three points and draw line segments to connect the pointsand make a triangle. Label the vertices of the triangle A, B, andC. Now describe the new coordinates of points A, B, and C after thefollowing transformations:
Translation of point A around the origin
90° rotation around point B
Reflection of the triangle across the x-axis
Detail your work and tell what the coordinates of all of therelevant points are.
Choose two coordinate points. On a sheet of paper or in agraphing utility, graph the segment that connects the two points.Now choose a ratio. Divide the segment into two parts according toyour ratio. Detail your work and tell what the coordinates of allof the relevant points are.
Choose two different coordinate points. On a sheet of paper orin a graphing utility, graph the line that connects the twopoints.
Write the equation of this line in slope intercept form. Labelit line A.
Now create a new line in slope intercept form that is parallelto line A and that passes through the origin. Label it lineB.
Now create a third line in slope intercept form that isperpendicular to line A and passes through the y-intercept of lineA. Label it line C.
