Write the Equation of the Line: Given two points

Front

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

Back

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

Front

How do you calculate the slope (m) 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 y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

Given two points (x1, y1) and (x2, y2), how can you write the equation of the line?

Back

First, calculate the slope (m) using m = (y2 - y1) / (x2 - x1). Then, use the point-slope form y - y1 = m(x - x1) to write the equation.

Front

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

Back

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

Front

How do you convert the point-slope form to slope-intercept form?

Back

To convert, solve for y: y = mx - mx1 + y1.

Front

What does it mean for two lines to be parallel?

Back

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

Front

What does it mean for two lines to be perpendicular?

Back

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

Front

How can you find the equation of a line given its slope and y-intercept?

Back

Use the slope-intercept form: y = mx + b, substituting the given slope (m) and y-intercept (b).

Front

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

Back

The slope indicates the steepness of the line and the direction it moves: positive slope means the line rises, negative slope means it falls.