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 (x₁, y₁) is a point on the line and m is the slope.

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 and the direction it goes (positive slope means the line rises, negative slope means it falls).

Front

Given the equation y - 3 = 2(x + 4), what is the slope?

Back

The slope is 2.

Front

For the equation y + 1 = 2(x - 5), what point does the line pass through?

Back

The line passes through the point (5, -1).

Front

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

Back

To convert from point-slope form (y - y₁ = m(x - x₁)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the slope of the line represented by the equation y + 1 = -3(x - 5)?

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, which is used to define the line's position.

Front

How can you identify the slope from the equation y - 3 = 2(x + 4)?

Back

The slope is the coefficient of (x - x₁), which in this case is 2.

Front

What does it mean if the slope of a line is negative?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.