5.1 and 5.2 Review

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all the equations true simultaneously.

Front

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

Back

The slope of a line represents the rate of change of the y-value with respect to the x-value, indicating how steep the line is.

Front

What is the y-intercept in 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

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points, calculate the slope (m) using (y2 - y1)/(x2 - x1) and then use the point-slope form: y - y1 = m(x - 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 if a system of equations has no solution?

Back

If a system of equations has no solution, it means that the lines represented by the equations are parallel and never intersect.

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the one that is changed or controlled in an experiment, while the dependent variable is the one that is measured or affected.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the point of intersection of two lines?

Back

The point of intersection of two lines is the point where the two lines cross, representing the solution to the system of equations.

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.