Welcome Back Warm-Up

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as the ratio of the change in the y-coordinate to the change in the x-coordinate (rise over run).

Front

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

Back

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

Front

What does the y-intercept represent 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

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation: y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine the rate of change from a linear graph?

Back

The rate of change is represented by the slope of the line on the graph.

Front

What does a negative slope indicate about a linear relationship?

Back

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

Front

What is the formula for a linear function based on a table of values?

Back

A linear function can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The y-intercept often represents the starting value or initial condition of a situation before any changes occur.

Front

What is the significance of the slope in a real-world scenario, such as a gardener watering a lawn?

Back

The slope represents the rate at which water is being used, indicating how many gallons are used per minute.

Front

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

Back

A larger absolute value of the slope indicates a steeper line, while a slope of zero indicates a horizontal line.