Slope from a graph

Front

What is the definition of slope in a graph?

Back

The slope of a line in a graph represents the rate of change of the y-coordinate with respect to the x-coordinate. It is calculated as the rise (change in y) over the run (change in x).

Front

How do you calculate 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 a positive slope indicate about a line on a graph?

Back

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

Front

What does a negative slope indicate about a line on a graph?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no change in the y-value as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero in the slope formula.

Front

If a line has a slope of 1, what does this mean?

Back

A slope of 1 means that for every unit increase in x, the y-value also increases by the same amount, resulting in a 45-degree angle line.

Front

How can you determine the slope from a graph visually?

Back

To determine the slope visually, select two points on the line, count the vertical rise and horizontal run between them, and use the rise/run ratio.

Front

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

Back

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

Front

What is the significance of the y-intercept in a graph?

Back

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