## Standards with the same topic and subject but for other grades

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 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.

Understand the connections between proportional relationships, lines, and linear equations.

Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Solve word problems leading to equations of the form ๐ฑ๐น + ๐ฒ = ๐ณ and ๐ฑ(๐น + ๐ฒ) = ๐ณ, where ๐ฑ, ๐ฒ, and ๐ณ are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Verify experimentally the properties of rotations, reflections, and translations:

Angles are taken to angles of the same measure.