Writing equations from 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 does the y-intercept represent in a linear equation?

Back

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

Front

Given two points, how can you find the equation of the line that passes through them?

Back

To find the equation of the line, first calculate the slope using the two points, then use one of the points to solve for the y-intercept, and finally write the equation in slope-intercept form.

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 equation from standard form to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y to get y = (-A/B)x + (C/B).

Front

What is the formula for the y-intercept (b) when given the slope and a point on the line?

Back

The y-intercept (b) can be found using the formula b = y - mx, where (x, y) is the point on the line and m is the slope.

Front

What is the relationship between the slopes of parallel and perpendicular lines?

Back

Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.

Front

How can you verify if a point lies on a given line?

Back

To verify if a point (x, y) lies on a line, substitute the x-value into the equation of the line and check if the resulting y-value matches the y-coordinate of the point.

Front

What is the first step in writing the equation of a line from two points?

Back

The first step is to calculate the slope (m) using the coordinates of the two points.