Linear Key Features

Front

What is the definition of 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 linear equation represent?

Back

The slope represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the x-intercept of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, represented as (a, 0) in the equation.

Front

How do you find the y-intercept from the equation y = 2/5x - 2?

Back

Set x = 0. The y-intercept is y = -2, so the point is (0, -2).

Front

How do you find the x-intercept from the equation y = 2/5x - 2?

Back

Set y = 0. Solve 0 = 2/5x - 2 to find x = 5, so the point is (5, 0).

Front

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

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a linear graph?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a linear graph?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) is the y-intercept, indicating where the line crosses the y-axis.