What is this grid called?
The coordinate plane. This is a 2-dimensional Cartesian coordinate system.
What are the dark lines called?
The x- and y-axes.
What does the O represent?
The origin
What are the coordinates of the endpoints of this line segment?
(2,3) and (9,8)
How would you calculate the midpoint of this line segment?
(3.5,2.5)
The midpoint is calculated by finding the midpoint along the x-axis and the midpoint along the y-axis separately.
Midpoint along x-axis: (9-2)/2 = 3.5
Midpoint along y-axis: (8-3)/2 = 2.5
How do you calculate the length of this line segment?
About 8.6
The length is found using the distance formula which is equivalent to the Pythagorean theorem.
How do you calculate the slope of this line segment?
5/7
You should expect that the slope is less than 1. If the slope of the line segment were 1, then the line segment would cross through the corner of each grid square.
What is the name of the point where it would cross the y-axis if it were extended?
The y-intercept
How would you calculate where the line would cross the y-axis?
The equation of the line is y = mx + b
You know two points on the line (2,3) and (9,8). You also know the slope, 5/7.
You plug in a point into the line equation: 3 = (5/7)2 + b, and solve for b.
What would be the formula for the line?
y = (5/7)x + 11/7
How would you find the area between the line segment and the x-axis?
Break the area into a rectangle and a triangle.
The area of the rectangle is 3 x 7 = 21
The area of the triangle is (bh)/2 = (7 x 5)/2 = 17.5
The total area is 21 + 17.5 = 38.5
What quadrant is this line segment in? What quadrant would it not pass through if it were extended?
It is in quadrant I. It would not pass through quadrant IV.
The quadrants are numbered in counterclockwise order, which is the direction that an angle grows as it gets bigger.
CoMo Science 
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