3.6 - Lv1 - Write Linear Equations

Front

What is the formula to calculate the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a positive slope indicate about the direction of a line on a graph?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about the direction of a line on a graph?

Back

A negative slope indicates that as the x-coordinate increases, the y-coordinate decreases, meaning the line falls from left to right.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x (denominator) is zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because there is no change in y (numerator) as x changes.

Front

How do you determine the slope from a graph of a line?

Back

To determine the slope from a graph, select two points on the line, find the rise (change in y) and run (change in x), and use the formula m = rise/run.

Front

If a line passes through the points (3, 4) and (3, 8), what is the slope?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

Front

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

Back

The slope represents the rate of change between two variables, which can be used to analyze trends, make predictions, and understand relationships in various contexts.

Front

How can you find the slope of a line using a table of values?

Back

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

Front

What is the slope of the line that passes through the points (1, 2) and (4, 5)?

Back

The slope is (5 - 2) / (4 - 1) = 3 / 3 = 1.