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 - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

Front

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

Back

In the point-slope form y - y_1 = m(x - x_1), the slope m is the coefficient of (x - x_1).

Front

What does the term 'perpendicular lines' mean in the context of slopes?

Back

Two lines are perpendicular if the product of their slopes is -1. If one line has a slope m, the other line's slope will be -1/m.

Front

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

Back

To convert to slope-intercept form, simplify: y = 3x + 3 + 2, which gives y = 3x + 5.

Front

What is the significance of the point (x_1, y_1) in the point-slope form?

Back

The point (x_1, y_1) represents a specific point through which the line passes.

Front

If a line has a slope of 2, what is the slope of a line perpendicular to it?

Back

The slope of a line perpendicular to a line with slope 2 is -1/2.

Front

Write the point-slope form for a line with slope -4 passing through the point (2, 3).

Back

The point-slope form is y - 3 = -4(x - 2).

Front

What is the slope of the line represented by the equation y + 5 = 2(x - 3)?

Back

The slope of the line is 2.

Front

How do you determine if a given equation is in point-slope form?

Back

An equation is in point-slope form if it can be expressed as y - y_1 = m(x - x_1), where m is the slope and (x_1, y_1) is a point on the line.

Front

What is the slope-intercept form of a line?

Back

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.