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 from two points (x₁, y₁) and (x₂, y₂)?

Back

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

Front

Given the point (4, 5) and a slope of 2, write the equation in point-slope form.

Back

y - 5 = 2(x - 4).

Front

What does the slope represent in a linear equation?

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 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

Convert the point-slope equation y - 3 = 4(x + 1) to slope-intercept form.

Back

y = 4x + 7.

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

Back

Substitute the x-value of the point into the equation and see if the resulting y-value matches the y-value of the point.

Front

Write the point-slope form for a line with slope -3 passing through the point (2, 1).

Back

y - 1 = -3(x - 2).