Question

What is the equation of the line that passes through the point (4, 3) and is perpendicular to the line x + y = 4?

Answer 1

ANSWER


`y - x = - 1`

Step-by-step explanation

The required equation passes through:

(4,3) and is perpendicular to x+y=4.

Rewrite the given equation in slope-intercept form:


`y = - x + 4`

The slope of this line is -1.

The slope of the required line is perpendicular to this line, so we find the negative reciprocal of this slope.


`m= - (1)/( - 1) = 1`

The equation of the line can be found using:


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

We substitute the slope and point to obtain:


`y - 3 = 1(x - 4)`

We simplify to get:


`y - 3 = x - 4`


`y - x = - 4 + 3`

The required equation is


`y - x = - 1`