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 the formula: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

Front

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

Back

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

Front

Convert the point-slope form y - 2 = 3(x - 1) into slope-intercept form.

Back

y = 3x - 1.

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.

Front

Write the point-slope form for a line with slope 2 that passes through the point (3, 4).

Back

y - 4 = 2(x - 3).

Front

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

Back

The slope is -2.

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

Write the equation in point-slope form for a line with slope -1/2 that passes through the point (2, 3).

Back

y - 3 = -1/2(x - 2).

Front

How do you convert the equation y - 1 = 4(x + 2) into standard form?

Back

4x - y = -9.

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.