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 identify the slope from a point-slope equation?

Back

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

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line is decreasing; as x increases, y decreases.

Front

How do you convert point-slope form to slope-intercept form?

Back

To convert point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the slope of a line that passes through the points (2, 3) and (4, 7)?

Back

The slope is calculated as (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 2.

Front

Write the point-slope form of the line with slope 2 that passes through the point (1, 4).

Back

The point-slope form is y - 4 = 2(x - 1).

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, which is used to define the line's position.

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal; there is no change in y as x changes.

Front

How do you find the slope between two points?

Back

The slope is found using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line represented by the equation y + 2 = 3(x - 1)?

Back

The slope is 3, as it is the coefficient of (x - 1) in the point-slope form.