Question

Consider the line y=2x−3. Find the equation of the line that is perpendicular to this line and passes through the point (7,4). Find the equation of the line that is parallel to this line 'and passes through the point (7,4). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line: Equation of parallel line:

Answer 1

The equation of the line perpendicular to y=2x-3 and passing through (7, 4) is y = -1/2x + 7.5, and the equation of the line parallel to it and passing through the same point is y = 2x - 10.

Step-by-step explanation:

The question involves finding the equations of lines that are perpendicular and parallel to the given line y=2x−3, which has a slope of 2.

To find the equation of a line perpendicular to it, we need a slope that is the negative reciprocal of 2, which is −1/2.

Using the point-slope form, the equation of the perpendicular line that passes through the point (7, 4) is y − 4 = −1/2(x − 7), which simplifies to y = −1/2x + 7.5.

Conversely, the equation of a line parallel to the given line will have the same slope of 2.

So, the equation of the parallel line passing through (7, 4) is also derived using the point-slope form, becoming y − 4 = 2(x − 7), and simplifying to y = 2x − 10.