Linear Graphs

Front

What is a linear graph?

Back

A linear graph is a graph that represents a linear equation, showing a straight line on a coordinate plane.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate, indicating how steep the line is.

Front

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

Back

m = (y2 - y1) / (x2 - x1)

Front

What does 'b' represent in the equation y = mx + b?

Back

'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

How do you find the y-intercept from a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the difference between positive and negative slopes?

Back

A positive slope indicates that as x increases, y also increases. A negative slope indicates that as x increases, y decreases.

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where x remains constant while y changes.

Front

Write the equation of a line with a slope of 2 and a y-intercept of 3.

Back

y = 2x + 3

Front

If a line has the equation y = -4x + 5, what is the slope?

Back

The slope is -4.