Point-Slope Form

Front

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

Back

The point-slope form of a linear equation is given by the formula: 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; it indicates how steep the line is.

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, and it is used as a reference to write the equation in point-slope form.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates that the line is horizontal.

Front

If a line has an undefined slope, what does that indicate about the line?

Back

An undefined slope indicates that the line is vertical.

Front

How do you find the slope of a line given two points (x₁, y₁) and (x₂, y₂)?

Back

The slope (m) can be calculated using the formula: m = (y₂ - y₁) / (x₂ - x₁).

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.

Front

What is the relationship between perpendicular lines in terms of slope?

Back

Perpendicular lines have slopes that are negative reciprocals of each other (m₁ * m₂ = -1).

Front

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

Back

y - 3 = 4(x - 2).