Question

C. Find the equation of the line perpendicular to
y = 14x-5 and passing through (2,-3).

Answer 1

`y = -4x + 5`

Explanation:

We want to find the equation of the line that is perpendicular to:

`\displaystyle y = (1)/(4) x - 5`

And which passes through the point (2, -3).

Recall that the slopes of perpendicular lines are negative reciprocals of each other.

In other words, since the slope of the original line is 1/4, the slope of the perpendicular line will be -4.

We are also given that it passes through the point (2, -3). Hence, we can consider using the point-slope form:

`\displaystyle y - y_1 = m(x- x_1)`

Substitute:

`\displaystyle y - (-3) = -4 (x - (2))`

Simplify:

`y + 3 = -4(x - 2)`
`y = -4x + 5`

Distribute:

`y + 3 = -4x +8`

And subtract:

`y = -4x + 5`

In conclusion, our equation is:

`y = -4x + 5`