TEKS 8.5I

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = 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) can be calculated using the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the two points.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

What is a function in mathematical terms?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

How can you determine if a relationship is linear from a graph?

Back

A relationship is linear if the graph forms a straight line.

Front

What is the meaning of the slope in a real-world context?

Back

The slope represents the rate of change; for example, in a salary function, it indicates how much the salary increases per mile driven.

Front

What is the significance of the x-value in a function?

Back

The x-value represents the independent variable, which is the input of the function.

Front

How do you interpret the equation y = mx + b in a real-world scenario?

Back

In a real-world scenario, y represents the dependent variable (output), x represents the independent variable (input), m is the rate of change, and b is the starting value.

Front

What is the relationship between the weight of pecans and their cost in a linear function?

Back

In a linear function relating weight and cost, the cost increases proportionally with the weight, represented by the slope.

Front

How can you derive a linear equation from two data points?

Back

To derive a linear equation from two points, first calculate the slope using the points, then use one point to solve for the y-intercept.