Review: Point-Slope Form

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is given by the equation: 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 slope-intercept form to point-slope form?

Back

To convert from slope-intercept form (y = mx + b) to point-slope form, identify a point (x₁, y₁) on the line and use the slope m in the point-slope formula.

Front

Given the point (4, -7) and slope m = -1/4, write the equation in point-slope form.

Back

y + 7 = -1/4(x - 4)

Front

Given the point (-2, -1) and slope m = -3, write the equation in point-slope form.

Back

y + 1 = -3(x + 2)

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

Identify the slope from the equation y - 1 = 4(x + 2).

Back

The slope is 4.

Front

For the equation y - 3 = 2(x + 4), what point does the line contain?

Back

The line contains the point (-4, 3).

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 can 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 relationship between point-slope form and slope-intercept form?

Back

Point-slope form can be rearranged to slope-intercept form (y = mx + b) by solving for y.