Writing Linear 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 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 slope of a line represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x = 0; it is the point where the line crosses the y-axis.

Front

How can you find the y-intercept of a linear equation if you have the slope and a point on the line?

Back

You can use the point-slope form of the equation, y - y1 = m(x - x1), to find the y-intercept by substituting the point and solving for b.

Front

What is the significance of a negative slope in a linear equation?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

What is the significance of a positive slope in a linear equation?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

How do you convert a linear 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 isolate it on one side of the equation.

Front

What is the formula for writing the equation of a line given two points?

Back

First, calculate the slope using m = (y2 - y1) / (x2 - x1), then use the point-slope form y - y1 = m(x - x1) to write the equation.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope; they never intersect.