Linear Equations from Graphs

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you find the y-intercept from a graph?

Back

The y-intercept is the point where the line crosses the y-axis. It can be found by looking at the value of y when x is 0.

Front

What is the formula for calculating the slope between two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does a positive slope indicate about a line?

Back

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

Front

What is the significance of a slope of zero?

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 and y can change.

Front

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

Back

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

Front

What is the y-intercept in the equation y = 2/3x + 1?

Back

The y-intercept is 1, which is the value of y when x is 0.