Slope & Intercepts

Front

What is the definition of the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

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

Front

How do you find the x-intercept of a linear equation?

Back

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

Front

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

Back

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

Front

What is the x-intercept of the equation y = 2x + 6?

Back

The x-intercept is -3, or (-3, 0).

Front

What is the y-intercept of the equation y = 2x + 6?

Back

The y-intercept is 6, or (0, 6).

Front

What does a positive slope indicate about a line?

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 line?

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 y-intercept in a real-world context?

Back

The y-intercept represents the value of y when x is zero, often indicating the starting point or initial condition in real-world scenarios.

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).