Checkpoint 5B: Writing Linear equations given two points

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope means the line rises, negative slope means it falls).

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be 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. It is represented by the value of b in the equation y = mx + b.

Front

How can you write the equation of a line given two points?

Back

1. Find the slope using the two points. 2. Use one of the points and the slope to write the equation in point-slope form: y - y1 = m(x - x1). 3. Rearrange to slope-intercept form if needed.

Front

What is point-slope form of a linear equation?

Back

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

Front

What is slope-intercept form of a linear equation?

Back

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 determine if a point lies on a line given by an equation?

Back

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

Front

What is the significance of a zero slope?

Back

A zero slope indicates a horizontal line, meaning there is no change in y as x changes. The equation of such a line is y = b, where b is a constant.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, meaning there is no change in x as y changes. The equation of such a line is x = a, where a is a constant.