Question

Which of the following is the equation of a line that is perpendicular to the line given by 8x + 12y = 13 and passes through the point (6,8)?

Option 1: y = $x - 6
Option 2: y = -3x - 1
Option 3: y = şx - 1
Option 4: y = x - 1

Answer 1

The equation of the line that is perpendicular to 8x + 12y = 13 and passes through (6,8) is y = (3/2)x + 1.

Step-by-step explanation:

To find the equation of a line that is perpendicular to the line given by 8x + 12y = 13 and passes through the point (6,8), we need to determine the slope of the given line and then find the negative reciprocal of that slope.

The given equation can be rearranged to the slope-intercept form y = mx + b, where m is the slope. In this case, the slope is -8/12 = -2/3. The negative reciprocal of -2/3 is 3/2.

Therefore, the equation of the line that is perpendicular to the given line and passes through the point (6,8) is y = (3/2)x + b. To find the value of b, substitute the coordinates of the point (6,8) into the equation. 8 = (3/2)(6) + b. Solving for b, we get b = 1.

So, the equation of the perpendicular line is y = (3/2)x + 1.