Question

Given the equation of a line: -x + 6y = 12, answer the following questions.

1. Rewrite the equation of this line to slope-intercept form.
2. What is the slope of this line?
3. Write the equation of the line parallel to this line passing through the point (6, 10).
4. What is the slope of the line perpendicular to this line? Keep your slopes in fraction form; use the '/' bar.

Answer 1

answer is :the line is 12 and 53

Answer 2

The slope-intercept form of the given equation is y = 1/6x + 2, the slope is 1/6, the equation of a parallel line passing through (6, 10) is y = 1/6x + 9, and the slope of the perpendicular line is -6.

Step-by-step explanation:

1. To rewrite the equation -x + 6y = 12 in slope-intercept form, solve for y. This gives us y = x/6 + 2 or y = 1/6x + 2. In slope-intercept form, the equation is y = mx + b where m is the slope and b is the y-intercept.

2. The slope of the line is the coefficient of x, which is 1/6.

3. A line parallel to the given line will have the same slope, so the slope is 1/6. The equation of this line can be found using the point-slope form, which is y - y1 = m(x - x1). Substituting the point (6, 10) and slope 1/6, we get y - 10 = 1/6(x - 6). To rewrite in slope-intercept form, simplify to get y = 1/6x + 9.

4. The slope of a line perpendicular to a given line is the negative reciprocal of the original slope. Therefore, the slope of the perpendicular line is -6.