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

How do you identify the slope from the equation in point-slope form?

Back

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

Front

What is the slope of the line represented by the equation y + 9 = 3(x - 1)?

Back

The slope of the line is 3.

Front

If a line has a slope of -3, what does this indicate about the line's direction?

Back

A slope of -3 indicates that the line descends from left to right, meaning for every 1 unit increase in x, y decreases by 3 units.

Front

What point is represented by the equation y - 5 = 3(x + 2)?

Back

The point (-2, 5) is on the line represented by the equation.

Front

How can you convert the 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 does the term 'slope' represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

In the equation y + 5 = -3(x - 6), what point lies on the line?

Back

The point (6, -5) lies on the line.

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 in the coordinate plane.

Front

How do you find a point on a line given its equation in point-slope form?

Back

To find a point on the line, you can substitute a value for x into the equation and solve for y.