[MA2019] REG-8 (8) 9 :
9. Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.
a. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.
b. Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.
c. Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.
d. Given that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts. [MA2019] REG-8 (8) 12 :
12. Solve systems of two linear equations in two variables by graphing and substitution.
a. Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of intersection on their graphs because points of intersection satisfy both equations simultaneously.
b. Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems. [MA2015] (8) 13 :
13 ) Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8-F3]
Example: The function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4), and (3,9), which are not on a straight line.
[MA2019] REG-8 (8) 27 :
27. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane. [MA2019] (6) 11 :
11. Find the position of pairs of integers and other rational numbers on the coordinate plane.
a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.
b. Identify (a,b) and (a,-b) as reflections across the x-axis.
c. Identify (a,b) and (-a,b) as reflections across the y-axis.
d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.