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 m is the slope and (x₁, y₁) is a point on the line.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do 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 slope of the line represented by the equation y + 9 = 3(x - 1)?

Back

The slope of the line is 3.

Front

How do you convert the equation y - y₁ = m(x - x₁) to slope-intercept form?

Back

To convert to slope-intercept form (y = mx + b), solve for y: y = mx + (y₁ - mx₁).

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, and it is used to anchor the equation in the point-slope form.

Front

If a line has a slope of -2, what does this indicate about its direction?

Back

A slope of -2 indicates that the line descends from left to right, meaning as x increases, y decreases.

Front

What is the equation in point-slope form for a line with slope 4 that passes through the point (2, 3)?

Back

The equation is: y - 3 = 4(x - 2).

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope. If m₁ = m₂, the lines are parallel.

Front

What is the equation in point-slope form for a line that passes through (5, -1) with a slope of 2?

Back

The equation is: y + 1 = 2(x - 5).