Writing in Point-Slope Form 1

Front

What is point-slope form?

Back

Point-slope form is a way to express the equation of a line using a point on the line and its slope. The formula is: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you identify a point from a point-slope equation?

Back

In the equation y - y1 = m(x - x1), the point (x1, y1) can be identified directly from the equation.

Front

What does the slope 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

Convert the point-slope equation y - 2 = 3(x + 6) to slope-intercept form.

Back

y = 3x + 16.

Front

What is the slope of the line represented by the equation y - 8 = 2/3(x - 4)?

Back

The slope is 2/3.

Front

Write the point-slope form of a line with slope -1 passing through the point (2, 5).

Back

y - 5 = -1(x - 2).

Front

How do you find the y-intercept from a point-slope equation?

Back

To find the y-intercept, convert the point-slope form to slope-intercept form (y = mx + b) and identify b.

Front

What is the significance of the coordinates in the equation y + 1 = 3/4(x + 4)?

Back

The coordinates (-4, -1) are the point through which the line passes.

Front

If a line has a slope of 2 and passes through (3, 4), what is its point-slope form?

Back

y - 4 = 2(x - 3).

Front

How do you determine if a point lies on a line given in point-slope form?

Back

Substitute the x-coordinate of the point into the equation and check if the resulting y-value matches the y-coordinate of the point.