Point Slope Form of a Line

Front

What is the point-slope form of a line?

Back

The point-slope form of a line 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

What does the slope represent in a linear equation?

Back

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

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

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

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 anchor the equation in the point-slope form.

Front

Convert the point-slope form to slope-intercept form: y - 2 = 3(x - 1).

Back

The slope-intercept form is y = 3x - 1.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates that the line is horizontal.

Front

If a line has an undefined slope, what does that indicate about the line?

Back

An undefined slope indicates that the line is vertical.

Front

Write the point-slope form of a line with slope 2 that passes through the point (3, 5).

Back

y - 5 = 2(x - 3).

Front

What is the slope of the line represented by the equation y + 4 = 3(x - 2)?

Back

The slope of the line is 3.

Front

How do you 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. If the equation holds true, the point lies on the line.