Fall Semester Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. Solutions are the points where the equations intersect.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

Rearrange the equation to isolate y: y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of the line represented by the equation 2x - 3y = 10?

Back

Front

What is a function?

Back

A relation where each input (x-value) has exactly one output (y-value).

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What does it mean if a system of equations has infinite solutions?

Back

It means the equations represent the same line, and every point on the line is a solution.

Front

How do you solve the equation 4(2a + 3) = 3(a - 1)?

Back

Distribute and simplify to find a = -3.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line: positive slope rises, negative slope falls.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis (x=0).