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 the slope represent in a linear equation?

Back

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

Front

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

Back

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

Front

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

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

Convert the point-slope equation y - 3 = 2(x + 4) to slope-intercept form.

Back

y = 2x + 11.

Front

What is the y-intercept in the equation y = 2x - 11?

Back

The y-intercept is -11, which is the point where the line crosses the y-axis.

Front

Given the equation y + 1 = -3(x - 5), what is the slope?

Back

The slope is -3.

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

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 used to define the line's position.

Front

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

Back

Two lines are parallel if they have the same slope.