Point-Slope Form

Front

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

Back

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

Front

If the slope m = 3 and the point is (1, 7), what is the point-slope form of the equation?

Back

y - 7 = 3(x - 1)

Front

How do you identify the slope from a point-slope equation?

Back

The slope m is the coefficient of (x - x₁) in the equation y - y₁ = m(x - x₁).

Front

What does the point (x₁, y₁) represent in the point-slope form?

Back

The point (x₁, y₁) represents a specific point on the line.

Front

How can you convert a point-slope equation to slope-intercept form?

Back

To convert, solve for y: y = mx - mx₁ + y₁.

Front

What is the slope of the line represented by the equation y - 2 = 4(x + 8)?

Back

The slope is 4.

Front

Given the equation y + 4 = 3(x + 3), what is the y-intercept?

Back

The y-intercept is -1 (when x = 0, y = -1).

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

If a line has a slope of -2 and passes through the point (3, 5), what is the point-slope form?

Back

y - 5 = -2(x - 3)

Front

How do 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 check if the resulting y-value matches the y-value of the point.