Equation of a Line given two points

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a line equation (y = mx + b). It is calculated as the change in y divided by the change in x (rise/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 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.

Front

What does the y-intercept represent in the equation of a line?

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 (y = mx + b).

Front

Given points (4, 5) and (2, -1), what is the slope of the line?

Back

The slope is m = (5 - (-1)) / (4 - 2) = 6 / 2 = 3.

Front

Write the equation of the line in slope-intercept form through (4, 5) and (2, -1).

Back

The equation is y = 3x - 7.

Front

How do you convert the slope and a point into the equation of a line?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the formula for the point-slope form of a line?

Back

The point-slope form is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Front

If a line has a slope of 0, what does that indicate?

Back

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

Front

If a line has an undefined slope, what does that indicate?

Back

An undefined slope indicates a vertical line, meaning there is no change in x as y changes.