Writing Linear 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) from 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 (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), what is the slope of the line?

Back

The slope m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

If the slope of a line is -3 and it passes through the point (1, 2), what is the equation of the line?

Back

Using the point-slope form: y - 2 = -3(x - 1) simplifies to y = -3x + 5.

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

What does a negative slope indicate about the relationship between x and y?

Back

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

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope.

Front

How can you determine if two lines are perpendicular using their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

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

Back

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