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 m is the slope and (x₁, y₁) is a point on the line.

Front

What does 'm' represent in the point-slope form?

Back

In the point-slope form, 'm' represents the slope of the line.

Front

How do you find 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 y-intercept of a line?

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

How can you convert point-slope form to slope-intercept form?

Back

To convert, solve for y: y - y₁ = m(x - x₁) becomes y = mx - mx₁ + y₁.

Front

What is the significance of the point (x₁, y₁) in point-slope form?

Back

The point (x₁, y₁) is a specific point on the line used to define the line's equation.

Front

If a line has a slope of 2 and passes through the point (3, 4), what is its point-slope form?

Back

The point-slope form is y - 4 = 2(x - 3).

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined.

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is 0.

Front

How do you determine if a point lies on a line given in point-slope form?

Back

Substitute the x and y coordinates of the point into the equation and check if the equation holds true.