Interpreting Linear Graphs

Front

What is the y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis. In the equation y = mx + b, b represents the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line measures its steepness and direction. It is calculated as the change in y divided by the change in x (rise/run).

Front

What does a slope of 1/2 indicate?

Back

A slope of 1/2 indicates that for every 2 units you move horizontally to the right, the line rises 1 unit vertically.

Front

What is the equation of a line in slope-intercept form?

Back

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

Front

How do you find the slope from two points?

Back

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

Front

What does the slope represent in a real-world context?

Back

In a real-world context, the slope represents the rate of change between two variables. For example, it can indicate cost per item or speed.

Front

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

Back

The y-intercept indicates the value of y when x is zero, providing a starting point for the line on the graph.

Front

How can you determine the equation of a line from a graph?

Back

To determine the equation of a line from a graph, identify the slope and the y-intercept, then use the slope-intercept form y = mx + b.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as one variable increases, the other variable decreases, showing an inverse relationship.

Front

What is the formula for calculating the y-intercept from a slope and a point?

Back

To calculate the y-intercept (b) from a slope (m) and a point (x, y), use the formula: b = y - mx.