Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation ๐บ = ๐ฎ๐น for a line through the origin and the equation ๐บ = ๐ฎ๐น + ๐ฃ for a line intercepting the vertical axis at ๐ฃ.
Expressions and Equations
Understand the connections between proportional relationships, lines, and linear equations.
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Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation ๐บ = ๐ฎ๐น for a line through the origin and the equation ๐บ = ๐ฎ๐น + ๐ฃ for a line intercepting the vertical axis at ๐ฃ.
Use similar triangles to explain why the slope ๐ is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation ๐ฆ = ๐๐ฅ for a line through the origin and the equation ๐ฆ = ๐๐ฅ + ๐ for a line intercepting the vertical axis at ๐.
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation ๐บ = ๐ฎ๐น for a line through the origin and the equation ๐บ = ๐ฎ๐น + ๐ฃ for a line intercepting the vertical axis at ๐ฃ.
Interpret ๐ฆ = ๐๐ฅ + ๐ as defining a linear equation whose graph is a line with ๐ as the slope and ๐ as the ๐ฆ-intercept.
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. Derive the equation ๐ฆ = ๐๐ฅ for a line through the origin and the equation ๐ฆ = ๐๐ฅ + ๐ for a line intercepting the vertical axis at (0, ๐).
