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

Given the equation y - 4 = -1/3(x - 7), what point does the line pass through?

Back

The line passes through the point (7, 4).

Front

How do you write the equation of a line in point-slope form given a slope and a point?

Back

To write the equation in point-slope form, use the formula y - y₁ = m(x - x₁), substituting m for the slope and (x₁, y₁) for the given point.

Front

What is the slope of the line represented by the equation y + 3 = 1(x + 2)?

Back

The slope of the line is 1.

Front

If a line has a slope of 1/2 and passes through the point (-2, 1), how is the equation written in point-slope form?

Back

The equation is written as y - 1 = 1/2(x + 2).

Front

What does the variable 'm' represent in the point-slope form of a linear equation?

Back

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

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 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 that the equation represents.

Front

How do you find the slope between two points, such as (-2, -3) and (4, 3)?

Back

The slope (m) is calculated using the formula m = (y₂ - y₁) / (x₂ - x₁). For the points (-2, -3) and (4, 3), m = (3 - (-3)) / (4 - (-2)) = 6 / 6 = 1.

Front

What is the first step in writing the equation of a line in point-slope form?

Back

The first step is to determine the slope of the line using two points or given slope.