Graphing Systems

Front

What is the definition of slope in a linear equation?

Back

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

Front

How do you determine if an ordered pair is a solution to a system of equations?

Back

An ordered pair (x, y) is a solution to a system of equations if it satisfies all equations in the system when substituted for x and y.

Front

What does it mean if a system of equations has no solution?

Back

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

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane, where each point on the line represents a solution to the equation.

Front

What is the significance of the y-intercept in 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

How can you find the intersection point of two lines graphically?

Back

To find the intersection point of two lines graphically, plot both lines on the same coordinate plane and identify the point where they cross.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

Front

How can you determine the slope of a line given its equation in standard form (Ax + By = C)?

Back

To find the slope from the standard form, rearrange the equation into slope-intercept form (y = mx + b) and identify the coefficient of x as the slope.

Front

What is the relationship between the slopes of parallel lines?

Back

The slopes of parallel lines are equal; they have the same steepness and will never intersect.