Writing Equations in 2 Variables

Front

What is an equation in two variables?

Back

An equation in two variables is a mathematical statement that shows the relationship between two variables, typically represented as x and y. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope means the line rises, negative slope means it falls).

Front

How do you find the y-intercept of an equation?

Back

The y-intercept of an equation is found by setting x to 0 and solving for y. It is the point where the line crosses the y-axis.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the difference between dependent and independent variables?

Back

The independent variable is the one that is changed or controlled in an experiment (usually x), while the dependent variable is the one that is measured or affected (usually y).

Front

Write the equation for a line with a slope of 2 and a y-intercept of 3.

Back

The equation is y = 2x + 3.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they represent the same line on a graph.

Front

How can you graph a linear equation?

Back

To graph a linear equation, you can find two or more points that satisfy the equation and plot them on a coordinate plane, then draw a line through those points.

Front

What is a function?

Back

A function is a relation between a set of inputs (x-values) and a set of possible outputs (y-values) where each input is related to exactly one output.

Front

How do you write an equation from a word problem?

Back

To write an equation from a word problem, identify the variables, determine the relationship between them, and express that relationship mathematically.