1B 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 determine the y-intercept from a linear equation in slope-intercept form?

Back

In the slope-intercept form of a linear equation, y = mx + b, the y-intercept is the value of b, which is the point where the line crosses the y-axis.

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 of equations, indicating the values of the variables that satisfy all equations in the system.

Front

How can you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, use the slope to find another point, and draw a straight line through the points.

Front

What does it mean if two lines are parallel in a system of linear equations?

Back

If two lines are parallel, it means they have the same slope but different y-intercepts, indicating that there is no solution to the system as they never intersect.

Front

What does it mean if two lines are coincident in a system of linear equations?

Back

If two lines are coincident, they lie on top of each other, meaning they have the same slope and y-intercept, resulting in infinitely many solutions.

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

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

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.

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).