Ch 7.4: Writing & Graphing Equations in Two-Variables Flashcard

Front

What is a linear equation in two variables?

Back

A linear equation in two variables is an equation that 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, indicating how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0, representing the point where the line crosses the y-axis.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, then use the slope to find another point and draw the line.

Front

What does the coordinate point (2,10) represent in a graph?

Back

The coordinate point (2,10) represents the position where x is 2 and y is 10 on the graph.

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 (usually y).

Front

What does the equation y = 2x + 1 represent?

Back

This equation represents a line with a slope of 2 and a y-intercept of 1.

Front

How can you determine if a point lies on a line represented by an equation?

Back

To determine if a point lies on a line, substitute the x-value of the point into the equation and see if the resulting y-value matches the y-value of the point.

Front

What is a table of values in relation to linear equations?

Back

A table of values lists pairs of x and y values that satisfy a linear equation, showing how y changes as x changes.

Front

What does the equation y = 5x + 1 indicate about the relationship between x and y?

Back

This equation indicates that for every increase of 1 in x, y increases by 5, plus an additional 1.