Interpreting Linear Equations

Front

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

Back

The y-intercept represents the value of y when x is 0, indicating the starting point of the line on the y-axis.

Front

What is the x-intercept in a set of ordered pairs?

Back

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0.

Front

How do you determine the initial value in a linear growth situation?

Back

The initial value is represented by the y-intercept in the equation, indicating the starting amount before any changes occur.

Front

What is the equation for the total cost of a holiday meal for x people, including a delivery fee?

Back

y = 30 + 12.5x, where 30 is the delivery fee and 12.5 is the cost per person.

Front

What does the rate of change indicate in a linear equation?

Back

The rate of change indicates how much the dependent variable (y) changes for a unit change in the independent variable (x).

Front

What is the slope of a line?

Back

The slope is the ratio of the rise (change in y) to the run (change in x), representing the steepness of the line.

Front

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

Back

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

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

What is the significance of the point (0, b) in a linear equation y = mx + b?

Back

The point (0, b) is the y-intercept, representing the value of y when x is 0.

Front

How do you interpret the slope in a real-world context?

Back

The slope represents the rate of change in a real-world scenario, such as speed, growth rate, or cost per item.