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 write the equation of a line in point-slope form given a slope and a point?

Back

To write the equation in point-slope form, use the formula y - y₁ = m(x - x₁), substituting m for the slope and (x₁, y₁) for the given point.

Front

Given the slope m = 3 and the point (1, -5), write the equation in point-slope form.

Back

The equation is: y + 5 = 3(x - 1).

Front

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

Back

The point (x₁, y₁) represents a specific point on the line, which is used to determine the line's equation.

Front

If a line has a slope of -3 and passes through the point (-2, -1), what is the point-slope form of the equation?

Back

The equation is: y + 1 = -3(x + 2).

Front

How can you identify the point that a line passes through from the point-slope form equation?

Back

In the equation y - y₁ = m(x - x₁), the point that the line passes through is (x₁, y₁).

Front

What is the slope of the line represented by the equation y - 4 = -1/3(x - 7)?

Back

The slope of the line is -1/3.

Front

How do you convert the point-slope form to slope-intercept form?

Back

To convert to slope-intercept form (y = mx + b), solve for y in the point-slope equation.

Front

Write the point-slope form of the line that contains the points (-2, -3) and (4, 3).

Back

The equation is: y + 3 = 1(x + 2).

Front

What does the slope represent in the context of a linear equation?

Back

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