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

Front

Given the equation y + 1 = -3(x - 5), what is the slope of the line?

Back

The slope of the line is -3.

Front

How do you convert the 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 the point (x1, y1) represent in the point-slope form?

Back

The point (x1, y1) represents a specific point on the line.

Front

If a line has a slope of 1/2 and passes through the point (-2, 1), what is the point-slope form of the equation?

Back

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

Front

How do you find the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), substituting the slope and the coordinates of the point.

Front

What is the slope of a line that passes through the points (1, -5) and (4, -7)?

Back

The slope m is calculated as (y2 - y1) / (x2 - x1) = (-7 - (-5)) / (4 - 1) = -2/3.

Front

Write the point-slope form of a line with slope m = 3 that goes through the point (1, -5).

Back

The point-slope form is y + 5 = 3(x - 1).

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.