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 convert the slope-intercept form to point-slope form?

Back

To convert from slope-intercept form (y = mx + b) to point-slope form (y - y1 = m(x - x1)), you can choose a point (x1, y1) on the line and substitute it into the point-slope formula.

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, indicating how steep the line is and the direction it goes (positive or negative).

Front

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

Back

The slope (m) between two points 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, and it is used as a reference point to write the equation in point-slope form.

Front

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

Back

A line with a slope of 0 is horizontal, meaning it does not rise or fall as it moves along the x-axis.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x (denominator) is 0, leading to division by zero.

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, find the vertical change (rise) and the horizontal change (run), and use the formula m = rise/run.

Front

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

Back

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

Front

How do you write the equation of a line in point-slope form given a slope and a point?

Back

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