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: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.

Front

How do you find the slope of a line given 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 variable 'm' represent in the point-slope form?

Back

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

Front

If a line has a slope of 1/2, what does this indicate about the line's steepness?

Back

A slope of 1/2 indicates that for every 2 units you move horizontally to the right, the line rises 1 unit vertically.

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, which is used to define the line's position in the coordinate plane.

Front

Convert the point-slope form y - 2 = 4(x + 8) to slope-intercept form.

Back

To convert to slope-intercept form, expand and simplify: y = 4x + 32 + 2, which gives y = 4x + 34.

Front

What is the slope of the line represented by the equation y + 1 = -3(x - 5)?

Back

The slope of the line is -3.

Front

How can you determine if a point lies on the line given by the equation y - 2 = 4(x + 8)?

Back

Substitute the x and y coordinates of the point into the equation. If the equation holds true, the point lies on the line.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope.

Front

What is the relationship between the slopes of perpendicular lines?

Back

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