Writing equations from two points

Front

What is the formula for the slope (m) of a line given two points (x1, y1) and (x2, y2)?

Back

m = (y2 - y1) / (x2 - x1)

Front

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

Back

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 and a point on the line?

Back

Use the formula b = y - mx, where (x, y) is the point on the line.

Front

What does the term 'linear equation' refer to in mathematics?

Back

An equation that models a straight line, typically in the form y = mx + b.

Front

How can you determine if two points lie on the same line?

Back

Calculate the slope between the two points; if the slopes are equal, they lie on the same line.

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 rises, while a negative slope falls.

Front

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

Back

Calculate the slope (m) using the coordinates of the two points.

Front

If a line has a slope of 0, what does this indicate about the line?

Back

The line is horizontal and does not rise or fall.

Front

What is the relationship between the slope of a line and its angle of inclination?

Back

The slope is the tangent of the angle of inclination; a steeper line has a larger slope.

Front

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

Back

Solve for y to isolate it on one side of the equation.