Linear Systems 1

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (y = mx + b). It is calculated as the rise over run, or the change in y divided by the change in x.

Front

How do you find the slope from two points?

Back

To find the slope (m) from two points (x1, y1) and (x2, y2), use the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented as 'b' in the equation of a line (y = mx + b).

Front

How do you identify the y-intercept from an equation?

Back

In the equation of a line in slope-intercept form (y = mx + b), the y-intercept is the value of 'b'.

Front

What does it mean for a system of linear equations to be consistent?

Back

A system of linear equations is consistent if it has at least one solution, meaning the lines represented by the equations intersect at one or more points.

Front

What does it mean for a system of linear equations to be inconsistent?

Back

A system of linear equations is inconsistent if it has no solutions, meaning the lines represented by the equations are parallel and never intersect.

Front

What is the elimination method in solving linear equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the substitution method in solving linear equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find at least two points that satisfy the equation, plot them on a coordinate plane, and draw a straight line through the points.

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.