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

What does 'm' represent in the point-slope form?

Back

'm' represents the slope of the line, indicating the steepness and direction of the line.

Front

How do you identify a point from the point-slope form equation y - 4 = -1/3(x - 7)?

Back

The point is (7, 4), which is derived from the equation in the form y - y₁ = m(x - x₁).

Front

What is the slope of the line represented by the equation y - 3 = 2(x + 4)?

Back

The slope (m) is 2.

Front

If a line passes through the point (-4, 3) and has a slope of 2, what is the point-slope form of the equation?

Back

The equation is y - 3 = 2(x + 4).

Front

What is the significance of the point (4, -7) in the equation y + 7 = -1/4(x - 4)?

Back

The point (4, -7) is the point through which the line passes, and the slope is -1/4.

Front

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

Back

To convert, solve for y: y - y₁ = m(x - x₁) becomes y = mx + (y₁ + m(x₁)).

Front

What does it mean if the slope 'm' is negative in a point-slope equation?

Back

A negative slope indicates that the line descends from left to right.

Front

What is the relationship between the slope and the steepness of a line?

Back

A larger absolute value of 'm' indicates a steeper line, while a smaller absolute value indicates a gentler slope.

Front

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

Back

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