Point-Slope Form

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 convert Point-Slope Form to Slope-Intercept Form?

Back

To convert from Point-Slope Form (y - y₁ = m(x - x₁)) to Slope-Intercept Form (y = mx + b), solve for y.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What are opposite reciprocals in the context of slopes?

Back

Opposite reciprocals are two numbers whose product is -1. If one slope is m, the other is -1/m.

Front

If a line has a slope of 2, what is the slope of a line perpendicular to it?

Back

The slope of a line perpendicular to a line with slope 2 is -1/2.

Front

What is the significance of the point (x₁, y₁) in Point-Slope Form?

Back

The point (x₁, y₁) is a specific point through which the line passes.

Front

How do you find the slope from two points (x₁, y₁) and (x₂, y₂)?

Back

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

Front

What is the equation of a line with slope -3 passing through (6, 1) in Point-Slope Form?

Back

The equation is y - 1 = -3(x - 6).

Front

What is the Slope-Intercept Form of the equation y + 5 = -3(x - 6)?

Back

The Slope-Intercept Form is y = -3x + 13.

Front

What does the term 'linear equation' mean?

Back

A linear equation is an equation that represents a straight line when graphed, typically in the form y = mx + b.