Learning Check 31 Retake: 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 two points into point-slope form?

Back

To convert two points (x₁, y₁) and (x₂, y₂) into point-slope form, first calculate the slope m = (y₂ - y₁) / (x₂ - x₁), then use one of the points in the equation y - y₁ = m(x - x₁).

Front

What is the slope of the line represented by the equation y + 3 = -4(x - 9)?

Back

The slope of the line is -4.

Front

Given the equation y + 6 = 10(x - 9), what point is used to write this equation?

Back

The point used is (9, -6).

Front

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

Back

y + 3 = 1(x + 2).

Front

What does the term 'slope' represent in a linear equation?

Back

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

Front

If the slope is 5 and the line passes through the point (-1, -3), what is the equation in point-slope form?

Back

y + 3 = 5(x + 1).

Front

How can you identify the point used in a point-slope equation?

Back

The point used in a point-slope equation is the (x₁, y₁) pair that is derived from the equation format y - y₁ = m(x - x₁).

Front

What is the relationship between point-slope form and slope-intercept form?

Back

Point-slope form can be converted to slope-intercept form (y = mx + b) by solving 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 helps define the line's position.