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

Front

How do you identify the slope from the point-slope form equation?

Back

In the equation y - y₁ = m(x - x₁), the slope m is the coefficient of (x - x₁).

Front

What does the point (5, -1) represent in the equation y + 1 = -3(x - 5)?

Back

The point (5, -1) is a point on the line represented by the equation y + 1 = -3(x - 5).

Front

How do you graph a line using point-slope form?

Back

To graph a line using point-slope form, start at the point (x₁, y₁) and use the slope m to determine the rise over run to find another point.

Front

What is the slope of the line represented by the equation y - 2 = 4(x + 8)?

Back

The slope of the line is 4.

Front

If a line has a slope of 3/4, what does this mean in terms of rise and run?

Back

A slope of 3/4 means that for every 4 units you move to the right (run), you move up 3 units (rise).

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.

Front

How can you convert point-slope form 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.

Front

What does it mean if a line has a negative slope?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.

Front

What is the first step to determine if a point lies on a line given in point-slope form?

Back

Substitute the x and y coordinates of the point into the equation and check if the equation holds true.