Understanding Slope and Intercepts

Front

What is the simple definition of slope?

Back

Slope is defined as the ratio of the rise (vertical change) to the run (horizontal change) between two points on a line, often expressed as rise/run.

Front

What is the y-intercept of the line y = 4x - 10?

Back

The y-intercept is the point where the line crosses the y-axis. For the equation y = 4x - 10, the y-intercept is -10.

Front

What is the slope in the equation y=2x + 3?

Back

The slope of the equation y = 2x + 3 is 2.

Front

Identify the y-intercept in the equation y = 5x - 8.

Back

The y-intercept in the equation y = 5x - 8 is -8.

Front

Find the slope of the line with the equation y = (1/2)x + 4.

Back

The slope of the line is 1/2.

Front

What does a positive slope indicate about a line?

Back

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

Front

What does a negative slope indicate about a line?

Back

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

Front

What is the formula to calculate slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

How can you determine the slope from a graph?

Back

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