Equation of a line given two points

Front

What is the formula to find the slope (m) of a line given 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 linear equation?

Back

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

Front

How do you find the y-intercept (b) of a line if you know the slope (m) and a point (x, y) on the line?

Back

You can find the y-intercept (b) by rearranging the slope-intercept form: b = y - mx.

Front

Given the points (2, 0) and (4, 4), find the slope of the line.

Back

The slope (m) is calculated as m = (4 - 0) / (4 - 2) = 2.

Front

Write the equation of the line in slope-intercept form that passes through the points (2, 0) and (4, 4).

Back

The equation is y = 2x - 4.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

How do you convert the standard form of a line (Ax + By = C) to slope-intercept form (y = mx + b)?

Back

Rearrange the equation to isolate y: y = (-A/B)x + (C/B).

Front

Given the points (-4, -2) and (-3, 5), find the equation of the line in slope-intercept form.

Back

The equation is y = 7x + 26.

Front

What does it mean if two lines are parallel in terms of their slopes?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Front

What does it mean if two lines are perpendicular in terms of their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1 (m1 * m2 = -1).