Search the California Content Standards

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

Standard:
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.

Cluster:
Analyze and solve linear equations and pairs of simultaneous linear equations.

Standard:
Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

Cluster:
Analyze and solve linear equations and pairs of simultaneous linear equations.

Standard:
Solve linear equations in one variable. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Cluster:
Analyze and solve linear equations and pairs of simultaneous linear equations.

Standard:
Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Cluster:
Analyze and solve linear equations and pairs of simultaneous linear equations.

Standard:
Analyze and solve pairs of simultaneous linear equations. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Cluster:
Analyze and solve linear equations and pairs of simultaneous linear equations.

Standard:
Analyze and solve pairs of simultaneous linear equations. Solve real-world and mathematical problems leading to to linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Cluster:
Build a function that models a relationship between two quantities. [Quadratic and exponential]

Standard:
Write a function that describes a relationship between two quantities. * Determine an explicit expression, a recursive process, or steps for calculation from a context. *

Cluster:
Build a function that models a relationship between two quantities. [Quadratic and exponential]

Standard:
Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. *

Cluster:
Build new functions from existing functions. [Quadratic, absolute value]

Standard:
Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Cluster:
Build new functions from existing functions. [Quadratic, absolute value]

Standard:
Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x^3.