STARK 1A 4.2 Practice: Systems from a Graph

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Front

What does the slope of a line represent in a linear equation?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

How do you identify the y-intercept from a linear equation in slope-intercept form (y = mx + b)?

Back

The y-intercept is the value of y when x = 0, represented by 'b' in the equation y = mx + b.

Front

What is the significance of the point of intersection in a system of linear equations?

Back

The point of intersection represents the solution to the system, where both equations are satisfied simultaneously.

Front

How can you determine if a system of equations has no solution?

Back

A system of equations has no solution if the lines are parallel, meaning they have the same slope but different y-intercepts.

Front

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

Back

A consistent system of equations has at least one solution, meaning the lines intersect at one or more points.

Front

What is the graphical representation of the equation y = -1/2x + 3?

Back

The graph is a straight line with a slope of -1/2 and a y-intercept of 3.

Front

How do you find 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 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 for two lines to be perpendicular?

Back

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