Slope from a Graph

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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-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 on a graph?

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 slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change is 0, leading to division by zero.

Front

How can you find the y-intercept from the equation of a line in slope-intercept form (y = mx + b)?

Back

The y-intercept is the value of y when x = 0, which is represented by the constant b in the equation.

Front

What is the x-intercept of a line?

Back

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0.

Front

How do you write the equation of a line given its slope and y-intercept?

Back

The equation can be written in slope-intercept form as 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 indicates the starting point of the line on the y-axis and represents the value of y when x is 0.