Question

22, 22, which equation can be used to find the equation of a line that passes through (2,-5) and is perpendicular to 2x + 3y = 7? (1 pt) y+5= 3(x-2) bly-s= (x+2) c) 4+5 = {(x-2) d) 4-5 - -}{(x+2) e) yts = = 2 2 3 (x-2) e) yes = ~2 (x+2)

Answer 1

Solution:-

Consider the equation of a line

2x + 3y = 7.

Let us convert it into slope intersect form.

2x + 3y = 7

3y = -2x +7

y = -2x/3 + 7/3

So, slope of this line is m' = -2/3 (on comparing with standard slope intercept form of an equation of line y = mx +c ).

Now, slope of a line(m) perpendicular to this given line is negative reciprocal of m'.

So, m= -1/m' = -1/(-2/3) = 3/2

We know that equation of line passing through (a, b) having spope m is

y - b = m(x - a)

So, equation of line passing through (2, -5) and having slope 3/2 is

y - (-5) = (3/2)(x - 2)

y + 5 = (3/2)(x -2).

Hence, the equation of line perpendicular to given line and passing through (2, -5) is

y + 5 = (3/2)(x -2)

(Correct option - a)