Analyze Linear Equations

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does the slope (m) represent in the slope-intercept form (y = mx + b)?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the definition of a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What does a positive slope indicate about a linear graph?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a linear graph?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.

Front

What is the significance of the x-intercept in a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, represented as (a, 0) in the equation.

Front

How can you find the y-intercept from a linear equation in standard form (Ax + By = C)?

Back

To find the y-intercept, set x = 0 and solve for y.

Front

What does a slope of zero indicate about a linear graph?

Back

A slope of zero indicates a horizontal line, meaning y remains constant regardless of x.

Front

What is an undefined slope?

Back

An undefined slope occurs in a vertical line where x remains constant, meaning the slope cannot be calculated.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert, solve for y in terms of x to get it into the form y = mx + b.