What is the equation of a line that passes through the point (2,7) and is perpendicular to the line whose equation is y = x/4 + 5

Answer 1

The slope of our line y = x/4 + 5 is m = 1/4

Since we're coming up with the equation of a line that is perpendicular, the slope of our perpendicular line is the opposite reciprocal of 1/4, or m = - 4/1 or m = 4

Now, we need to find out the y-intercept of our perpendicular line. To do that we plug in (2, 7) into x and y as well as - 4 into m in the following equation:

y = mx + b

7 = (- 4)(2) + b

7 = - 8 + b

15 = b

Thus, with m = - 4 and b = 15, the equation of our perpendicular line is:

y = - 4x + 15

Answer 2

The line perpendicular to this one will have a slope equal to the negative reciprocal. In the equation provided, the slope is 1/4. So m=-4 for the line perpendicular. Then you can use the following equation.

(y-y1)=m(x-x1) Plug in the values of (x1,y1) using the point provided. (2,7)

(y-7)=-4(x-2) Distribute

y-7=-4x+8 Add 7 to both sides

y-7+7=-4x+8+7 Simplify

y=-4x+15