Forms of a Line Flashcard

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented by the letter 'm'. It is calculated as the change in y (rise) divided by the change in x (run).

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of 'b' in the slope-intercept form.

Front

How do you convert an equation to slope-intercept form?

Back

To convert an equation to slope-intercept form, isolate y on one side of the equation to get it in the form y = mx + b.

Front

What are x- and y-intercepts?

Back

The x-intercept is the point where the line crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0).

Front

How can you find the x-intercept of an equation?

Back

To find the x-intercept, set y to 0 in the equation and solve for x.

Front

How can you find the y-intercept of an equation?

Back

To find the y-intercept, set x to 0 in the equation and solve for y.

Front

What is the equation of a line that passes through the point (5, 2) with a slope of -1/5?

Back

Using the point-slope form, the equation is y - 2 = -1/5(x - 5).

Front

What is the relationship between the slope and the angle of a line?

Back

The slope of a line is related to the angle it makes with the x-axis; a positive slope indicates an upward angle, while a negative slope indicates a downward angle.