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 convert a point-slope equation 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 slope (m) represent in a point-slope equation?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

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 as a reference to write the equation in point-slope form.

Front

How can you identify the slope from a point-slope equation?

Back

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

Front

What is the point-slope form equation for a line with slope 2 passing through the point (3, 5)?

Back

The point-slope form equation is y - 5 = 2(x - 3).

Front

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

Back

To graph a line using point-slope form, plot the point (x1, y1) on the graph, then use the slope (m) to find another point by moving up/down and left/right.

Front

What is the relationship between point-slope form and standard form of a linear equation?

Back

Point-slope form (y - y1 = m(x - x1)) can be converted to standard form (Ax + By = C) by rearranging the equation.

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points, first calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), then use one of the points in the point-slope form.

Front

What is the point-slope form equation for a line with slope -1 passing through the point (0, 0)?

Back

The point-slope form equation is y - 0 = -1(x - 0), or simply y = -x.