Point-Slope Form, Steepness, & Slope Meaning

Front

What is the Point-Slope Form of a linear equation?

Back

The Point-Slope Form is given by the equation: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

Front

How do you determine the steepness of a line?

Back

The steepness of a line is determined by its slope (m). A larger absolute value of m indicates a steeper 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 formula for calculating the slope between two points (x₁, y₁) and (x₂, y₂)?

Back

The slope (m) 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 is given by the equation: y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert from Point-Slope Form to Slope-Intercept Form?

Back

To convert, solve for y in the Point-Slope Form equation: y - y₁ = m(x - x₁) to get y = mx + b.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal, indicating that y remains constant regardless of x.

Front

If a line has an undefined slope, what does that mean?

Back

An undefined slope occurs in vertical lines, where x remains constant and y can take any value.