Writing equations from two points

Front

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

Back

The slope-intercept form is 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 as m = (y2 - y1) / (x2 - x1).

Front

What does the y-intercept (b) represent in the equation y = mx + b?

Back

The y-intercept b represents the point where the line crosses the y-axis.

Front

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

Back

y = 2x - 1.

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 find the y-intercept from two points?

Back

First, find the slope using the two points, then use one of the points and the slope to solve for b in the equation y = mx + b.

Front

Write the equation of the line that passes through (1, 2) and (3, 6).

Back

y = 2x.

Front

What is the formula for converting standard form Ax + By = C to slope-intercept form?

Back

Solve for y to get y = (-A/B)x + (C/B).

Front

If a line has a slope of -3 and passes through the point (0, 4), what is its equation?

Back

y = -3x + 4.

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.