1.

Graphing equations on a coordinate plane is a simple way to visually represent the relationship between the input values (x) of an equation and the output values (y). This visual representation allows us to make predictions, solve problems, find the point(s) that solve both equations (when there are two), and analyze many other useful business and everyday situations.

1. Name some real-life situations where graphing could be useful. Discuss your ideas. Name some real-life situations where finding the coordinates of the midpoint of a line segment could be useful.
2. 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 points and make a triangle. Label the vertices of the triangleA,B, andC. Now describe the new coordinates of pointsA,B, andCafter the following transformations:

• Translation of pointAaround the origin
• 90 rotation around pointB
• Reflection of the triangle across thex-axis

2. Detail your work and tell what the coordinates of all of the relevant points are.
4. Choose two coordinate points. On a sheet of paper or in a graphing utility, graph the segment that connects the two points. Now choose a ratio. Divide the segment into two parts according to your ratio. Detail your work and tell what the coordinates of all of the relevant points are.
5. Choose two different coordinate points. On a sheet of paper or in a graphing utility, graph the line that connects the two points.

• Write the equation of this line in slope intercept form. Label it lineA.
• Now make a new line in slope intercept form that is parallel to lineAand that passes through the origin. Label it lineB.
• Now make a third line in slope intercept form that is perpendicular to lineAand passes through they-intercept of lineA. Label it lineC.