Unit 3 Algebra I Test

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The slope (m) of a line given two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the line crosses the y-axis, represented by the value of b in the equation f(x) = mx + b.

Front

What does it mean for a function to have a zero?

Back

A zero of a function is a value of x for which the function f(x) equals zero. It represents the x-intercept of the graph of the function.

Front

How can you determine the zero of the function f(x) = 2x - 6?

Back

To find the zero of the function f(x) = 2x - 6, set f(x) to zero and solve for x: 0 = 2x - 6, which gives x = 3.

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 is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

Front

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

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables. A positive slope means the line rises, while a negative slope means it falls.

Front

How do you graph a linear equation?

Back

To graph a linear equation, you can find two or more points that satisfy the equation and plot them on a coordinate plane, then draw a straight line through the points.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.