TMS Linear Functions Mixed

Front

What is a linear function?

Back

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

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

What is the equation of a line with a slope of -5/3 and a y-intercept of -1?

Back

The equation is y = (-5/3)x - 1.

Front

How do you graph a linear equation?

Back

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

Front

What does it mean if a line has a positive slope?

Back

A line with a positive slope rises from left to right, indicating that as the x-value increases, the y-value also increases.

Front

What does it mean if a line has a negative slope?

Back

A line with a negative slope falls from left to right, indicating that as the x-value increases, the y-value decreases.

Front

How can you write an equation from a word problem involving a linear function?

Back

Identify the variables, determine the fixed costs and variable costs, and set up the equation based on the relationship described in the problem.

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.