Flashcardizz: Solutions to Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a point to be a solution to a linear equation?

Back

A point (x, y) is a solution to a linear equation if, when the x-value is substituted into the equation, the resulting y-value is equal to the y-value of the point.

Front

How do you determine if an ordered pair is a solution to a linear equation?

Back

Substitute the x-value of the ordered pair into the equation and see if the resulting y-value matches the y-value of the ordered pair.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

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 by the value of y when x = 0.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Front

How can you find the y-coordinate for a given x-coordinate in a linear equation?

Back

Substitute the x-coordinate into the linear equation and solve for y.

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 does it mean if a linear equation has no solution?

Back

A linear equation has no solution if the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a linear equation has infinitely many solutions?

Back

A linear equation has infinitely many solutions if the two equations represent the same line, meaning every point on the line is a solution.