23-24 ACP Review 2

Front

What is the rate of change in a linear function, and how is it represented in the equation y = mx + b?

Back

The rate of change in a linear function is the slope (m), which represents the change in y for a unit change in x. In the equation y = mx + b, m is the slope.

Front

How do you determine the range of a function from its graph?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. It can be determined by observing the lowest and highest points on the graph.

Front

What does it mean for y to be directly proportional to x?

Back

If y is directly proportional to x, it means that as x increases, y increases at a constant rate. This relationship can be expressed as y = kx, where k is a constant.

Front

How do you calculate a new value of y when given a proportional relationship and a new value of x?

Back

To calculate the new value of y, use the formula y = kx, where k is the constant of proportionality determined from the initial values.

Front

What is the formula to find the height of an object in direct variation with time?

Back

The height (h) can be expressed as h = kt, where k is the constant of variation and t is time.

Front

How do you set up a direct variation equation from given values?

Back

To set up a direct variation equation, identify the constant of variation (k) using known values, then express the relationship as y = kx.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

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

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

How do you interpret the slope in a real-world context, such as in cost per mile?

Back

In a real-world context, the slope represents the rate of change, such as the cost per mile in a taxi or Uber fare.