CM: Final test review (Linear eq)

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 m is -1/m. Therefore, the slope is 1/2.

Front

How do you find the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the equation of a line parallel to 5x + 2y = 1?

Back

First, rewrite in slope-intercept form: 2y = -5x + 1, so y = -\frac{5}{2}x + \frac{1}{2}. The slope is -\frac{5}{2}. Any line parallel will have the same slope.

Front

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

Back

The slope m is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the equation of a line that passes through the points (4, 5) and (12, 9)?

Back

First, find the slope: m = (9 - 5) / (12 - 4) = 1/2. Then use point-slope form: y - 5 = (1/2)(x - 4) which simplifies to y = (1/2)x + 3.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope.

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other.

Front

How do you convert the standard form of a line to slope-intercept form?

Back

To convert Ax + By = C to slope-intercept form (y = mx + b), solve for y: y = -\frac{A}{B}x + \frac{C}{B}.

Front

What is the slope of the line represented by the equation y = -3x - 8?

Back

The slope is -3.

Front

What is the y-intercept of the line y = -\frac{5}{2}x - 8?

Back

The y-intercept is -8.