Writing Equations of Lines given Various Information

Front

What is the slope of a line perpendicular to a line with a slope of 2?

Back

The slope of a line perpendicular to a line with slope 2 is -\frac{1}{2}.

Front

What is the slope-intercept form of a line?

Back

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = \frac{y2 - y1}{x2 - x1}.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

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

Front

Write the equation of a line with a slope of 3 that passes through the point (1, 2).

Back

The equation is y - 2 = 3(x - 1) or y = 3x - 1.

Front

What is the y-intercept of the line y = 4x + 5?

Back

The y-intercept is 5.

Front

How do you convert the standard form of a line Ax + By = C to slope-intercept form?

Back

To convert to slope-intercept form, solve for y: y = -\frac{A}{B}x + \frac{C}{B}.

Front

Write the equation of a line parallel to y = -x + 4 that passes through (2, 3).

Back

The equation is y - 3 = -1(x - 2) or y = -x + 5.

Front

What is the slope of the line represented by the equation 2x + 3y = 6?

Back

The slope is -\frac{2}{3}.