Graphing Linear Equations Flashcard

Front

What is the definition of a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed on a coordinate plane, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the x-intercept of a line represent?

Back

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

Front

What does the y-intercept of a line represent?

Back

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

Front

How do you find the slope of a line given two points?

Back

The slope (m) of a line given two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

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

Back

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

Front

How can you graph a linear equation using intercepts?

Back

To graph a linear equation using intercepts, plot the x-intercept and y-intercept on the coordinate plane and draw a straight line through these two points.

Front

What is the relationship between the slope and the direction of a line?

Back

A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right.

Front

What is the significance of a zero slope in a linear equation?

Back

A zero slope indicates a horizontal line, meaning that the y-value remains constant regardless of the x-value.

Front

What does it mean if a line has an undefined slope?

Back

An undefined slope indicates a vertical line, meaning that the x-value remains constant regardless of the y-value.

Front

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

Back

The equation of a line can be determined using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.