3.3 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 identify the slope from a point-slope equation?

Back

In the point-slope form y - y₁ = m(x - x₁), the slope is represented by the variable m.

Front

Given the equation y - 3 = 2(x + 4), what is the slope and what point does the line pass through?

Back

The slope is 2, and the line passes through the point (-4, 3).

Front

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

Back

The slope of the line is -3.

Front

How do you convert two points into point-slope form?

Back

To convert two points (x₁, y₁) and (x₂, y₂) into point-slope form, first calculate the slope m = (y₂ - y₁) / (x₂ - x₁), then use one of the points in the formula y - y₁ = m(x - x₁).

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 in the coordinate plane.

Front

How can you determine if a point lies on a line given in point-slope form?

Back

To determine if a point (x, y) lies on the line, substitute x and y into the point-slope equation and check if the equation holds true.

Front

What is the general process for writing an equation in point-slope form from a graph?

Back

Identify a point on the line and the slope of the line, then use the point-slope formula y - y₁ = m(x - x₁) to write the equation.

Front

What does the 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 and the direction it moves.

Front

How do you find the slope between two points?

Back

The slope between two points (x₁, y₁) and (x₂, y₂) is calculated using the formula m = (y₂ - y₁) / (x₂ - x₁).