Question

The graphs of the two lines 4x=3y+23 and 4y+3x= -19 A. do not intersect. B. are identical C. intersect at (-2,5) D.are perpendicular

Answer 1

Answer:

The correct option is D.

Step-by-step explanation:

The given equations are

$4x=3y+23$

$4y+3x=-19$

The slope intercept form of a line is

$y=mx+b$

where, m is slope and b is y-intercept.

Rewrite the given equations is the slope intercept form.

$y=\frac{4}{3}x-\frac{23}{3}$

$y=-\frac{3}{4}x-\fra{19}{4}$

Therefore the slope of first line is $\frac{4}{3}$ and the slope of second line is $-\frac{3}{4}$.

$m_1\times m_2=\frac{4}{3}\times =-\frac{3}{4}=-1$

Since the product of slopes of two perpendicular lines is -1, therefore we can say that both lines are perpendicular to each other. Option D is correct.