Linear Functions

Front

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

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

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

Back

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

Front

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

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 of the line represented by the equation y = mx + b?

Back

The slope (m) indicates the steepness of the line and the direction it goes; a positive slope rises to the right, while a negative slope falls to the right.

Front

How can you determine if a linear function is increasing or decreasing?

Back

A linear function is increasing if the slope is positive and decreasing if the slope is negative.

Front

What is a T-table in relation to linear functions?

Back

A T-table is a tool used to organize values of x and their corresponding y values for a linear function, helping to visualize the relationship.

Front

What does the equation y = -25x + 120 represent in a real-world context?

Back

This equation represents a situation where there are 120 gallons of water in a tank, and it releases water at a rate of 25 gallons per minute.

Front

How do you convert a linear equation from slope-intercept form to point-slope form?

Back

To convert, identify the slope (m) and y-intercept (b) from y = mx + b, then use a point on the line (x1, y1) to write it in point-slope form.

Front

What is the significance of the slope in a real-world scenario?

Back

The slope often represents a rate of change, such as cost per mile in a moving truck rental situation.

Front

How do you find the y-intercept from a linear equation in standard form?

Back

To find the y-intercept from Ax + By = C, set x = 0 and solve for y.