7. Writing Linear Functions

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented by the letter 'm'. It is calculated as the change in y (rise) divided by the change in x (run).

Front

How do you find the slope from a table of values?

Back

To find the slope from a table, select two points (x1, y1) and (x2, y2) and use the formula m = (y2 - y1) / (x2 - x1).

Front

What does the equation y = mx + b represent?

Back

This is the slope-intercept form of a linear equation, where 'm' is the slope and 'b' is the y-intercept.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, which can be expressed in the form y = mx + b.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by 'b' in the equation y = mx + b.

Front

How can you identify a linear graph?

Back

A linear graph will form a straight line when plotted on a coordinate plane.

Front

What does the equation x = a represent?

Back

This represents a vertical line on the graph where all points have the same x-coordinate 'a'.

Front

How do you determine if a graph is linear?

Back

Check if the graph forms a straight line; if it does, it is linear.

Front

What is the significance of the slope in real-world applications?

Back

The slope indicates the rate of change, such as speed in a distance-time graph or cost per item in a price graph.

Front

What is the formula to calculate the slope between two points?

Back

The formula is m = (y2 - y1) / (x2 - x1).