Equation of a Line

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is given by the equation: y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x. It indicates how steep the line is.

Front

How do you calculate the slope between 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 is the slope-intercept form of a linear equation?

Back

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

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form.

Front

If a line has a slope of 3/4, what does this indicate?

Back

A slope of 3/4 indicates that for every 4 units moved horizontally to the right, the line rises 3 units vertically.

Front

What is the significance of a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line descends from left to right, meaning as x increases, y decreases.

Front

How can you convert from point-slope form to slope-intercept form?

Back

To convert, solve for y in the point-slope equation: y - y_1 = m(x - x_1) to get y = mx + (y_1 - mx_1).

Front

What is the formula to find the y-intercept from the slope-intercept form?

Back

In the slope-intercept form y = mx + b, b is the y-intercept.