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 variable 'm' represent in the point-slope form?

Back

In the point-slope form, 'm' represents the slope of the line.

Front

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

Back

The slope 'm' can be calculated using the formula: m = (y₂ - y₁) / (x₂ - x₁).

Front

What is the slope of the line represented by the equation y - 1 = 4(x - 2)?

Back

The slope of the line is 4.

Front

If a line has a slope of -2, what does this indicate about its direction?

Back

A slope of -2 indicates that the line descends from left to right.

Front

What point does the line y + 3 = 5(x - 1) pass through?

Back

The line passes through the point (1, -3).

Front

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

Back

To convert to slope-intercept form (y = mx + b), solve for y: y - y₁ = m(x - x₁) becomes y = mx + (y₁ - mx₁).

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

Given the equation y - 2 = 3(x + 1), what is the slope?

Back

The slope is 3.

Front

Which of the following points lies on the line y - 4 = -1(x - 2)? (2, 4), (3, 3), (4, 2), (5, 1)

Back

The point (2, 4) lies on the line.