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 convert a point-slope equation 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 to isolate it on one side of the equation.

Front

What does the slope (m) represent in the point-slope form?

Back

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

Front

Given the point (2, 3) and a slope of 4, write the point-slope form of the equation.

Back

The point-slope form is: y - 3 = 4(x - 2).

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

If a line has a slope of -2 and passes through the point (1, 5), what is the point-slope form?

Back

The point-slope form is: y - 5 = -2(x - 1).

Front

How can you find the slope of a line given 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 point-slope form of the line that passes through (3, -5) and (5, -1)?

Back

The point-slope form is: y + 5 = 2(x - 3).

Front

Convert the point-slope equation y - 1 = -3(x - 6) to slope-intercept form.

Back

The slope-intercept form is: y = -3x + 13.

Front

What is the general process for converting from point-slope to standard form?

Back

To convert from point-slope form to standard form, rearrange the equation to the form Ax + By = C, where A, B, and C are integers.