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 find the slope from two points (x_1, y_1) and (x_2, y_2)?

Back

The slope (m) is calculated using the formula: m = (y_2 - y_1) / (x_2 - x_1).

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.

Front

Convert the point-slope equation y - 2 = 3(x + 4) to slope-intercept form.

Back

To convert to slope-intercept form, solve for y: y = 3x + 14.

Front

What is the slope of the line represented by the equation y + 1 = -2(x - 3)?

Back

The slope of the line is -2.

Front

Given the point-slope equation y - 5 = 4(x - 1), what is the y-intercept?

Back

The y-intercept is 1, found by converting to slope-intercept form: y = 4x - 4.

Front

Write the point-slope form for a line with slope 2 passing through the point (1, 3).

Back

The point-slope form is: y - 3 = 2(x - 1).

Front

What is the relationship between point-slope form and slope-intercept form?

Back

Point-slope form can be converted to slope-intercept form (y = mx + b) by solving for y.

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

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

Back

The point (x_1, y_1) is a specific point on the line that the equation represents.