Front

What is the slope in a linear equation?

Back

The slope is the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

Front

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

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the linear function on the y-axis.

Front

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

Back

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

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented 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 expression 2(5+x) represent in a real-world context?

Back

It represents the total time spent painting rooms, where 5 is the number of rooms painted on one day and x is the number of rooms painted on another day.

Front

How can you rearrange the formula T = 263p + 189q to solve for q?

Back

To solve for q, rearrange the formula to get q = (T - 263p) / 189.

Front

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

Back

Coefficients represent the relationship between the variables. For example, in y = mx + b, m indicates how much y changes for a unit change in x.

Front

What does it mean for two linear functions to have the same rate of change?

Back

It means they have the same slope. If two linear functions have the same slope, they will rise or fall at the same rate.

Front

What is the formula for calculating the total cost of items based on quantity and price?

Back

The total cost T can be calculated using the formula T = price * quantity.

Front

What is the relationship between the slope and the steepness of a line?

Back

The slope indicates the steepness of a line; a larger absolute value of the slope means a steeper line.