Question

Consider the line y=2x−6. Find the equation of the line that is parallel to this line and passes through the point (5,2). Find the equation of the line that is perpendicular to this line and passes through the point (5,2). Note that the ALEKS graphing calculator may be helpful in checking your answer.

Answer 1

To find the equation of a line parallel to y=2x-6 and passing through (5,2), use the same slope of 2 and the point-slope form of a line. The equation is y = 2x - 8. To find the equation of a line perpendicular to y=2x-6 and passing through (5,2), find the negative reciprocal of the slope. The equation is y = -1/2x + 9/2.

Step-by-step explanation:

To find the equation of a line parallel to the line y=2x-6 and passing through the point (5,2), we need to use the fact that parallel lines have the same slope. So, the slope of the parallel line will also be 2.

Using the point-slope form of a line, we can write the equation as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substituting the values, we get y - 2 = 2(x - 5).

Expanding the equation further, we get y - 2 = 2x - 10. Simplifying, we obtain the equation of the line parallel to y=2x-6 and passing through (5,2) as y = 2x - 8.

To find the equation of a line perpendicular to the line y=2x-6 and passing through the point (5,2), we need to find the negative reciprocal of the slope of the given line. The given line has a slope of 2, so the slope of the perpendicular line will be -1/2.

Using the point-slope form again, we can write the equation as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substituting the values, we get y - 2 = -1/2(x - 5).

Expanding the equation further, we get y - 2 = -1/2x + 5/2. Simplifying, we obtain the equation of the line perpendicular to y=2x-6 and passing through (5,2) as y = -1/2x + 9/2.