Perpendicular and Parallel Lines Through Points

Front

What is the slope of a line perpendicular to a line with slope \( m \)?

Back

The slope of a line perpendicular to a line with slope \( m \) is \( -\frac{1}{m} \).

Front

Write the equation of a line in slope-intercept form given a slope of 2 and a y-intercept of 3.

Back

The equation is \( y = 2x + 3 \).

Front

What is the slope of the line represented by the equation \( y = -3x + 5 \)?

Back

The slope is -3.

Front

If two lines have the same slope, what can we say about their relationship?

Back

The lines are parallel.

Front

What is the equation of a line parallel to \( y = 4x + 1 \ \) that passes through the point \( (2, 5) \)?

Back

The equation is \( y = 4x + 1 \).

Front

How do you find the slope of a line given two points \( (x_1, y_1) \) and \( (x_2, y_2) \)?

Back

The slope is calculated as \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Front

What is the equation of a line perpendicular to \( y = \frac{1}{2}x + 3 \ \) that passes through the point \( (0, 2) \)?

Back

The equation is \( y = -2x + 2 \).

Front

What is the relationship between the slopes of two perpendicular lines?

Back

The product of their slopes is -1.

Front

Write the equation of a line parallel to \( 3x + 2y = 6 \ \) that passes through the point \( (1, 2) \).

Back

The equation is \( y = -\frac{3}{2}x + \frac{7}{2} \).

Front

If a line has the equation \( y = 5x - 4 \), what is the slope of a line parallel to it?

Back

The slope is 5.