Equation from Two Points

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

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 points (x1, y1) and (x2, y2), how do you find the equation of the line in slope-intercept form?

Back

1. Calculate the slope (m) using m = (y2 - y1) / (x2 - x1). 2. Use one of the points to solve for b in the equation y = mx + b.

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

Write the equation of the line in slope-intercept form through the points (1, 2) and (3, 4).

Back

y = x + 1.

Front

What does it mean if the slope of a line is zero?

Back

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

Front

Write the equation of the line in slope-intercept form through the points (2, 3) and (4, 7).

Back

y = 2x - 1.

Front

What is the formula to convert a point-slope equation to slope-intercept form?

Back

Start with y - y1 = m(x - x1) and rearrange to y = mx + (y1 - mx1).

Front

How do you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope (m).