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 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 does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

If a line has a slope of 1/2, what does this mean in terms of rise over run?

Back

A slope of 1/2 means that for every 2 units you move horizontally (run), the line rises 1 unit (rise).

Front

Convert the point-slope form y - 2 = 3(x - 1) to slope-intercept form.

Back

The slope-intercept form is y = 3x - 1.

Front

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

Back

The point (x₁, y₁) is a specific point on the line that the equation describes.

Front

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

Back

Two lines are parallel if they have the same slope.

Front

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

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

Write the point-slope form of a line with slope -2 that passes through the point (4, 3).

Back

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

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is 0.